1
The correct condition for a linear equation in two variables is —
💡 Hint:
At least one variable must remain.
Explanation:
a and b must not both be zero.
Class 9 · Maths · Chapter 4 · बिहार बोर्ड (BSEB)CBSE · NCERT 2026-27
Linear Equations in Two Variables
Linear Equations in Two Variables
How to use this page:
1. Read — Form ax + by + c = 0 · Exercise 4.1 · solutions · Exercise 4.2 · graph · Exercise 4.3 · parallels to the axes · Exercise 4.4, diagram, worked example, board tip
2. Check — each lesson has its own questions; the number follows the lesson
3. Mastery ★ — all of that lesson correct. Redo the wrong ones
4. The memory figure shows the line x + y = 7 passing through the plotted points (0, 7) and (7, 0).
In the 15-chapter Bihar book this is chapter 4. Ganita Manjari 2026-27 uses a different order. Progress stays in this browser.
🏅 Your achievements — 0/6 badges
🔥 0day streak · longest 0
⭐ 0total XP · today 0
🎓 1level
Next level: 150 XP to goright answer +10 · after a hint +5 · review +6 · badge +25
Last 7 days:
Everything is saved in this phone/browser — no login.
- 1 The form ax + by + c = 0
- 2 Solutions and infinitely many pairs
- 3 The graph is a straight line
- 4 A point on the line is a solution
- 5 The axes and lines parallel to them
- 6 The line y = mx through the origin
- Chapter winner — every lesson at mastery ★
🎬 Shorts
This chapter has no Short on the channel yet, so ten empty cards are not shown. The notes, diagrams and checks are complete.
📄 PDF download — notes + answer key
The form ax + by + c = 0
रूप ax + by + c = 0 · Textbook 4.2 · Exercise 4.1
Two variables, each to the power oneNotes
The equation ax + by + c = 0 is a linear equation in two variables. a, b and c are real numbers. The condition is that a and b are not both zero. The power of x is 1 and the power of y is 1. x², y² or xy do not make the line of this chapter.
Write 2x + 3y = 12 as 2x + 3y − 12 = 0. Then a = 2, b = 3 and c = −12. The sign travels with the equation. Writing +12 would change the equation. In two variables, x = −5 is written x + 0·y + 5 = 0.
Worked exampleExample
Question: Write y = 2 as ax + by + c = 0 and give a, b and c.
Answer: Write y − 2 = 0 as 0·x + 1·y − 2 = 0. So a = 0, b = 1 and c = −2. b is not zero, so the ban on both being zero is not broken.
10-second revision
- The form ax + by + c = 0
- a and b are not both zero
- Power 1; not x² or xy
Board tip · BSEBBoard tip
When you take the sign of c, bring the equation to zero. In 2x + 3y = 12, c is −12, not +12.
Board tip · CBSEBoard tip
a = 0 is allowed if b is not zero. y = 2 is linear. 0·x + 0·y + 5 = 0 is not linear.
Check your understandingall correct = mastery ★
2
x² + y = 3 is a linear equation in two variables.
Explanation:
False — the power of x is 2. In a linear equation every variable has power 1.
3
When 2x + 3y = 12 is written equal to zero, c = ______.
💡 Hint:
12 comes to the left as a negative.
Explanation:
c = −12. The equation is 2x + 3y − 12 = 0.
4
The two-variable form of x = −5 is —
💡 Hint:
The coefficient of y is 0.
Explanation:
x + 0·y + 5 = 0.
5
Write 3y − 4 = 0 as ax + by + c = 0. Give a, b and c, and say why it is allowed.
Model answer (board format)
0·x + 3y − 4 = 0. a = 0, b = 3, c = −4. b is not zero, so a and b are not both zero. It is a linear equation in two variables.
Check your answer:
Solutions and infinitely many pairs
हल और अनंत युग्म · Textbook 4.3 · Exercise 4.2
A pair that makes the equation trueNotes
An ordered pair (x, y) that makes the equation true is a solution. In x + 2y = 6, put x = 2. Then 2 + 2y = 6, so y = 2. The pair (2, 2) is one solution. Put x = 0 and y = 3, the pair (0, 3). Put x = 4 and y = 1.
There are infinitely many such solutions. One variable is free and the other follows from it. Two different equations can pin one pair in a later class. In this chapter there is one equation.
Worked exampleExample
Question: Find one solution of x + 2y = 6 when x = 6. Take 1 unit = 1 cm on the axes.
Equation: x + 2y = 6
Substitution: 6 + 2y = 6, so 2y = 0 and y = 0. The solution is (6, 0).
Unit: the point is on the x-axis, 6 cm to the right of the origin.
10-second revision
- A solution is an ordered pair (x, y)
- One equation has infinitely many solutions
- Choose one variable and find the other
Board tip · BSEBBoard tip
When four solutions are asked, give four different pairs. Writing one pair four times is not an example of infinitely many solutions.
Board tip · CBSEBoard tip
Do not turn (2, 2) into the single number (2 + 2). A solution is a pair.
Check your understandingall correct = mastery ★
1
One solution of x + 2y = 6 is —
💡 Hint:
2 + 2·2 = 6.
Explanation:
(2, 2). 2 + 4 = 6.
2
x + 2y = 6 has only one solution.
Explanation:
False — (0, 3), (2, 2), (4, 1) and (6, 0) are all solutions. There are more.
3
In x + 2y = 6, if x = 0 then y = ______.
💡 Hint:
2y = 6.
Explanation:
y = 3. The pair is (0, 3).
4
Find two different solutions of x + y = 7. Show the substitution in each.
Model answer (board format)
Put x = 0, then y = 7, so (0, 7) is a solution. Put x = 7, then y = 0, so (7, 0) is a solution. Both make the equation true, and they are two of infinitely many.
Check your answer:
The graph is a straight line
ग्राफ एक सरल रेखा है · Textbook 4.4 · Exercise 4.3
Join the solutions and the line appearsNotes
The solutions (0, 3), (2, 2), (4, 1) and (6, 0) of x + 2y = 6 sit on one straight line on the graph. That is the graph of every linear equation in two variables.
Two solutions are enough to draw the line. Keep a third solution for a check. If it lands on the line, the working is right. Write the scale on both axes.
Worked exampleExample
Question: Through which two points would you draw the graph of x + y = 7? 1 unit = 1 cm.
Equation: x + y = 7
Substitution: when x = 0, y = 7, the point (0, 7). When y = 0, x = 7, the point (7, 0).
Unit: these intercepts are 7 cm on the y-axis and 7 cm on the x-axis. Join them.
10-second revision
- The graph is always a straight line
- Two points are enough for the line
- A third point is the check
Board tip · BSEBBoard tip
Leaving the points unjoined is half an answer. Joining them with a straight line is the graph.
Board tip · CBSEBoard tip
A curve, a parabola or a broken line is not the graph of this chapter. Power 1 means a line.
Check your understandingall correct = mastery ★
1
The graph of a linear equation in two variables is —
💡 Hint:
Infinitely many solutions lie on one line.
Explanation:
A straight line.
2
At least three solutions are compulsory before the line can be drawn.
Explanation:
False — two solutions are enough. A third is good for a check, not compulsory.
3
In x + y = 7, when x = 0 one point of the graph is ______.
💡 Hint:
y = 7.
Explanation:
(0, 7). Another easy point is (7, 0).
4
Which point lies on the line x + 2y = 6?
💡 Hint:
0 + 2·3 = 6.
Explanation:
(0, 3). At (3, 0), 3 is not 6.
5
Write two solutions of x + 2y = 6 and say how the graph is drawn.
Model answer (board format)
(0, 3) and (6, 0) are two solutions. Plot them and join them with a straight line. That is the graph. For a check, (2, 2) should also lie on the line.
Check your answer:
6
The graph of x + y = 7 passes through (0, 7) and (7, 0).
Explanation:
True — both pairs make the equation true.
A point on the line is a solution
रेखा पर बिंदु हल है · Textbook 4.4 · solution and point together
The line and the solutions are two faces of one factNotes
If a point lies on the graph, its coordinates are a solution of the equation. If a pair is a solution, the point lies on the line. A point off the line is not a solution. So a check means putting the coordinates into the equation.
Infinitely many lines can pass through one point. The point (1, 2) lies on x + y = 3, on y − x = 1, and also on y = 2x. One point does not fix one equation.
Worked exampleExample
Question: Is (1, 2) a solution of x + y = 4? 1 unit = 1 cm.
Equation: x + y = 4
Substitution: 1 + 2 = 3, and 3 ≠ 4.
Answer: (1, 2) is not a solution. The point is not on the line. The point 1 cm right and 2 cm up from the origin is off this line.
10-second revision
- A point on the line = a solution
- Off the line = not a solution
- Infinitely many lines through one point
Board tip · BSEBBoard tip
Before writing “the point is on the line”, show whether the sum equals the equation.
Board tip · CBSEBoard tip
The sentence “only one line passes through (1, 2)” is wrong. Give at least two equations in the example.
Check your understandingall correct = mastery ★
1
(1, 2) is a solution of which equation?
💡 Hint:
1 + 2 = 3.
Explanation:
x + y = 3.
2
A point that is not on the line can still be a solution of the equation.
Explanation:
False — the solutions and the points on the line are the same collection.
3
One line through (1, 2) is y − x = ______.
💡 Hint:
2 − 1 = 1.
Explanation:
1. y − x = 1.
4
Through one point, lines of linear equations can pass —
💡 Hint:
(1, 2) will satisfy many equations.
Explanation:
Infinitely many. One point does not fix the equation alone.
5
Does (3, 1) lie on x + 2y = 5? Show the substitution. Also write another equation through the same point.
Model answer (board format)
3 + 2·1 = 5, so (3, 1) lies on the line and is a solution. Another equation is x + y = 4, because 3 + 1 = 4. One point can lie on infinitely many lines.
Check your answer:
The axes and lines parallel to them
अक्ष और उनके समांतर रेखाएँ · Textbook 4.5 · Exercise 4.4
When one coordinate is fixed, the line is parallel to an axisNotes
Every point on the x-axis has ordinate 0, so the equation of the x-axis is y = 0. It can also be written 0·x + 1·y = 0. The equation of the y-axis is x = 0.
x = a is a vertical line, parallel to the y-axis and a units away from it. y = a is a horizontal line, parallel to the x-axis. In x = a the variable y is free, and in y = a the variable x is free. So these too are linear equations with infinitely many solutions.
Worked exampleExample
Question: Solve 2x + 1 = x − 3 and show it on the plane. 1 unit = 1 cm.
Solution: 2x − x = −3 − 1, so x = −4.
Plane: x + 0·y + 4 = 0. This is a line parallel to the y-axis, 4 cm to the left of the origin. Two solutions are (−4, 0) and (−4, 2). On the number line the same solution was the single point x = −4.
10-second revision
- y = 0 is the x-axis, x = 0 is the y-axis
- x = a is parallel to the y-axis
- y = a is parallel to the x-axis
Board tip · BSEBBoard tip
Do not write x = 3 as parallel to the x-axis. When x is fixed the line is vertical, so it is parallel to the y-axis.
Board tip · CBSEBoard tip
On the number line x = −4 is a point. On the Cartesian plane it is a line. Name the plane in the answer.
Check your understandingall correct = mastery ★
1
The equation of the y-axis is —
💡 Hint:
On this axis the abscissa is zero.
Explanation:
x = 0. y = 0 is the x-axis.
2
The line y = 5 is parallel to the x-axis.
Explanation:
True — the ordinate is fixed, so the line is horizontal.
3
The equation of the x-axis is y = ______.
💡 Hint:
The ordinate is zero.
Explanation:
y = 0.
4
The graph of x = −4 is —
💡 Hint:
x is fixed.
Explanation:
A vertical line parallel to the y-axis, 4 units to the left.
5
In every solution of x = 4 the value of y is the same.
Explanation:
False — x = 4 is fixed and y may be any real number.
6
What is the graph of y = −2? Write two solutions and the distance from the axis. 1 unit = 1 cm.
Model answer (board format)
The graph is a horizontal line parallel to the x-axis, 2 cm below the x-axis. Two solutions are (0, −2) and (3, −2). x may be anything.
Check your answer:
The line y = mx through the origin
मूल से गुजरती रेखा y = mx · Textbook 4.6 · summary
When the constant term is zeroNotes
Write y = mx as mx − y = 0. Here c = 0. Put x = 0 and y = 0. So the line passes through the origin. m tells the slope: when x grows by 1 unit, y changes by m units.
The force and acceleration example has the same form, y = kx. Here k is constant. The graph is a straight line through the origin. Change k and the slope changes, but the line still meets the origin.
Worked exampleExample
Question: On y = 2x, write the point when x = 3. 1 unit = 1 cm. Show that the origin is also on the line.
Equation: y = 2x
Substitution: y = 2·3 = 6. The point is (3, 6), 3 cm right and 6 cm up from the origin. When x = 0, y = 0, so (0, 0) is also a solution.
10-second revision
- y = mx passes through the origin
- When c = 0, (0, 0) is a solution
- m or k is the slope, and the line is still straight
Board tip · BSEBBoard tip
y = 2x + 3 does not pass through the origin. (0, 0) is a solution only when the constant term is zero.
Board tip · CBSEBoard tip
When the slope is asked, write “if x grows by one, how much y grows”. Only m = 2 is not enough if the meaning is missing.
Check your understandingall correct = mastery ★
1
The graph of y = 3x must pass through —
💡 Hint:
c = 0.
Explanation:
(0, 0). 0 = 3·0.
2
y = 2x + 1 passes through the origin.
Explanation:
False — when x = 0, y = 1, not the origin.
3
On y = 2x, when x = 3, y = ______.
💡 Hint:
Twice.
Explanation:
6. The point is (3, 6).
4
If k in y = kx is a mass, what is the graph like? For k = 4 and x = 2 find the point with the unit. 1 unit = 1 cm.
Model answer (board format)
The graph is a straight line through the origin. y = 4·2 = 8, so the point is (2, 8), 2 cm right and 8 cm up from the origin. A change in k changes the slope.
Check your answer:
❓ Full question bank — with answers and explanations — 65 questions
Pick a type. The 30 lesson checks are separate — each lesson has as many as its topic needs. All correct earns mastery ★.
BSEB modelpractice · not annual60 tried · 0 correctMultiple choiceMCQ130 tried · 0 correctTrue / falseTrue / false80 tried · 0 correctFill in the blanksFill80 tried · 0 correctMatchMatch20 tried · 0 correctAssertion–reasonAssertion–reason50 tried · 0 correctBalancingBalancing40 tried · 0 correctIdentifyIdentify20 tried · 0 correctShort and longVSA, SA, LA110 tried · 0 correctCBSE-stylenot a PYQ60 tried · 0 correct
No question is marked as a verified past paper. The BSEB set is a model for practice. CBSE items are CBSE-style, not a copy of any year’s paper.
Multiple choice
0/13Pick one option. A wrong try brings a hint.
1
In ax + by + c = 0 it is forbidden that —
💡 Hint:
One variable must remain.
Explanation:
a and b cannot both be zero.
2
In 2x + y = 5, a, b and c are —
💡 Hint:
Bring it to zero.
Explanation:
2x + y − 5 = 0, so c = −5.
3
A solution of x + 2y = 6 is —
💡 Hint:
0 + 2·3 = 6.
Explanation:
(0, 3).
4
The solutions of such an equation are —
💡 Hint:
One variable stays free.
Explanation:
Infinitely many ordered pairs.
5
The graph is —
💡 Hint:
Join two solutions.
Explanation:
A straight line.
6
The least number of solutions needed to draw the line is —
💡 Hint:
The third is a check.
Explanation:
Two.
7
(1, 2) is a solution of —
💡 Hint:
2 = 2·1.
Explanation:
y = 2x.
8
The equation of the x-axis is —
💡 Hint:
The ordinate is zero.
Explanation:
y = 0.
9
The line x = 5 is parallel to —
💡 Hint:
A vertical line.
Explanation:
The y-axis.
10
The line y = −3 is —
💡 Hint:
y is fixed.
Explanation:
Horizontal, parallel to the x-axis.
11
y = 4x must pass through —
💡 Hint:
The constant term is zero.
Explanation:
The origin (0, 0).
12
On the plane, the graph of 2x + 1 = x − 3 is —
💡 Hint:
A point on the number line, a line on the plane.
Explanation:
The line x = −4, parallel to the y-axis.
13
Which is not linear?
💡 Hint:
Look at the power and the product.
Explanation:
xy = 6 is not linear.
True or false
0/81
The equation can be linear when a = 0 and b = 2.
Explanation:
True — they are not both zero. The y term remains.
2
Every solution is a single number, not a pair.
Explanation:
False — a solution is an ordered pair (x, y).
3
Every point on the line is a solution of the equation.
Explanation:
True — and every solution is on the line.
4
x = 0 is the equation of the x-axis.
Explanation:
False — x = 0 is the y-axis. The x-axis is y = 0.
5
y = mx passes through the origin.
Explanation:
True — when x = 0, y = 0.
6
Only one line of a linear equation passes through a given point.
Explanation:
False — (1, 2) lies on infinitely many equations, such as x + y = 3 and y = 2x.
7
On the plane, x = −4 is parallel to the y-axis.
Explanation:
True — x is fixed and the line is vertical.
8
Three solutions make three different lines.
Explanation:
False — all the solutions of one equation lie on the same line.
Fill in the blanks
0/81
The standard form is ______ + by + c = 0.
💡 Hint:
ax.
Explanation:
a is the coefficient of x.
2
In x + 2y = 6, if x = 4 then y = ______.
💡 Hint:
1.
Explanation:
4 + 2y = 6.
3
The graph is a ______ line.
💡 Hint:
Straight.
Explanation:
Not a curve.
4
The equation of the y-axis is x = ______.
💡 Hint:
0.
Explanation:
The abscissa is zero.
5
The line x = a is parallel to the ______ axis.
💡 Hint:
The y-axis.
Explanation:
Vertical.
6
In y = mx, if m = 0 the line becomes the ______ axis.
💡 Hint:
The x-axis.
Explanation:
y = 0.
7
(0, 7) lies on the equation x + y = ______.
💡 Hint:
7.
Explanation:
0 + 7.
8
The solution of 2x + 1 = x − 3 is x = ______.
💡 Hint:
−4.
Explanation:
2x − x = −3 − 1.
Match
0/21
Match the equation with its line.
Column B: A. The x-axis · B. Parallel to the y-axis · C. Parallel to the x-axis · D. The y-axis
1. x = 0
2. y = 0
3. x = 4
4. y = 4
Explanation:
x = 0 is the y-axis, y = 0 the x-axis, x = 4 vertical, y = 4 horizontal.
2
Match the statement with the right fact.
Column B: A. An ordered pair · B. A straight line · C. Passes through the origin · D. Not linear
1. A solution
2. The graph
3. y = mx
4. a and b both 0
Explanation:
A solution is a pair, the graph is a line, y = mx meets the origin, and both zero is forbidden.
Assertion–reason
0/5Check both statements, then see whether the reason explains the assertion.
1
Assertion (A): x + 2y = 6 has infinitely many solutions.
Reason (R): Once one variable is chosen the other follows, and the choices are infinite.
Explanation:
Both are true and R is the correct reason.
2
Assertion (A): The graph is a straight line.
Reason (R): x = 0 is the equation of the y-axis.
Explanation:
Both are true, but R does not explain why the graph is a line.
3
Assertion (A): y = 0 is the x-axis.
Reason (R): On the x-axis the abscissa is always zero.
Explanation:
A is true. R is false — on the x-axis the ordinate is zero.
4
Assertion (A): xy = 9 is a linear equation in two variables.
Reason (R): In the linear form every variable has power 1 and a product of the variables is not a term.
Explanation:
A is false. R is true — this is why xy = 9 is not linear.
5
Assertion (A): (3, 0) does not lie on x + 2y = 6.
Reason (R): 3 + 2·0 = 3, which is not equal to 6.
Explanation:
Both are true and R is the correct check.
Coefficient practice
0/4These are not results of this maths chapter. They are only coefficient practice for H2 + O2 → H2O.
1
This is coefficient practice, not a result of this maths chapter. Fill coefficients for H2 + O2 making H2O (blank = 1). Match the count of hydrogen.
H2 + O2 → H2O
Explanation: 2H2 + O2 → 2H2O
2
This is coefficient practice, not a result of this maths chapter. Fill coefficients for H2 + O2 making H2O (blank = 1). Match the count of oxygen.
H2 + O2 → H2O
Explanation: 2H2 + O2 → 2H2O
3
This is coefficient practice, not a result of this maths chapter. Fill coefficients for H2 + O2 making H2O (blank = 1). This is not the equation of a line.
H2 + O2 → H2O
Explanation: 2H2 + O2 → 2H2O
4
This is coefficient practice, not a result of this maths chapter. Fill coefficients for H2 + O2 making H2O (blank = 1). A blank coefficient means 1.
H2 + O2 → H2O
Explanation: 2H2 + O2 → 2H2O
Classify
0/21
Place each equation as linear or not.
2x + y − 3 = 0
x² + y = 1
y = 4
xy + 1 = 0
Explanation:
Power 1 and separate terms are linear. x² and xy are not linear.
2
Place each line in its type.
x = 0
y = −2
y = 3x
y = 0
Explanation:
x = 0 is the y-axis. y = −2 and y = 0 are horizontal. y = 3x passes through the origin.
Very short answer
0/51
Define a linear equation in two variables in one line.
Model answer (board format)
ax + by + c = 0, where a, b, c are real and a, b are not both zero.
Check your answer:
2
Write two solutions of x + y = 5.
Model answer (board format)
(0, 5) and (5, 0). 0 + 5 = 5 and 5 + 0 = 5.
Check your answer:
3
What is the graph of such an equation?
Model answer (board format)
A straight line.
Check your answer:
4
Which lines are x = 0 and y = 0?
Model answer (board format)
x = 0 is the y-axis. y = 0 is the x-axis.
Check your answer:
5
Why does y = 5x pass through the origin?
Model answer (board format)
Putting x = 0 gives y = 0, so (0, 0) is a solution.
Check your answer:
Short answer
0/31
Write 2x − y = 4 in standard form. Find the solution when x = 2. With 1 unit = 1 cm, say where the point is.
Model answer (board format)
2x + (−1)y + (−4) = 0, so a = 2, b = −1, c = −4. When x = 2, 4 − y = 4, so y = 0. The point (2, 0) is on the x-axis, 2 cm to the right of the origin.
Check your answer:
2
How would you draw the graph of x + y = 7 from two points? Write a check with a third point.
Model answer (board format)
Plot (0, 7) and (7, 0) and join them. Check: when x = 3, y = 4, and (3, 4) should lie on the same line because 3 + 4 = 7.
Check your answer:
3
How does x = −4 look different on the number line and on the Cartesian plane?
Model answer (board format)
On the number line it is one point. On the plane x + 0·y + 4 = 0 is a line parallel to the y-axis, 4 units left of the origin. y takes infinitely many values.
Check your answer:
Long answer
0/31
Write four solutions of x + 2y = 6 in a table, describe the graph, and say why (1, 1) is not a solution.
Model answer (board format)
The solutions are (0, 3), (2, 2), (4, 1) and (6, 0). They lie on one straight line. Two points are enough to draw the line. At (1, 1), 1 + 2 = 3 ≠ 6, so the point is not on the line.
Check your answer:
2
Write three linear equations through (1, 2). Then say why one point does not fix a line, while two points do fix the graph of one equation.
Model answer (board format)
x + y = 3, y − x = 1 and y = 2x are all true at (1, 2). One point can lie on infinitely many lines. Two solutions of one equation fix that one line.
Check your answer:
3
Describe the lines y = 0, x = 0, x = 3, y = −2 and y = 2x separately. Write one solution of each.
Model answer (board format)
y = 0 is the x-axis, solution (2, 0). x = 0 is the y-axis, solution (0, 5). x = 3 is parallel to the y-axis, solution (3, 1). y = −2 is parallel to the x-axis, solution (1, −2). y = 2x passes through the origin, solution (1, 2).
Check your answer:
BSEB model paper · practice
0/6This model set is for practice. It is not a question from any year’s annual examination. Annual questions will be added only when a source page is available.
1
Which standard form is correct?
💡 Hint:
Move terms so the right side is zero.
Explanation:
x + y − 3 = 0. c = −3.
2
y = −4 is parallel to —
💡 Hint:
A horizontal line.
Explanation:
The x-axis.
3
At least ______ solutions are needed to draw the line.
💡 Hint:
2.
Explanation:
The third is a check.
4
(6, 0) is a solution of x + 2y = 6.
Explanation:
True — 6 + 0 = 6.
5
Write two solutions of y = 3x and one line about the graph.
Model answer (board format)
(0, 0) and (1, 3). The graph is a straight line through the origin.
Check your answer:
6
This is coefficient practice, not a result of linear equations. Balance H2 + O2 making H2O by filling coefficients (blank = 1).
H2 + O2 → H2O
Explanation: 2H2 + O2 → 2H2O
CBSE-style questions
0/6These are competency-based practice questions. They are not copies of a CBSE paper.
1
A student calls x = 5 parallel to the x-axis. The right correction is —
💡 Hint:
If x is fixed the line is upright.
Explanation:
x = 5 is vertical, so it is parallel to the y-axis.
2
In a shop a notebook costs x and a pen costs y. One meaning of x + y = 20 is —
💡 Hint:
One equation, two variables.
Explanation:
There are infinitely many solutions and they lie on a straight line.
3
Assertion (A): (2, 2) does not lie on x + 2y = 6.
Reason (R): A pair is a solution only when the coordinates make the equation true.
Explanation:
A is false — 2 + 4 = 6, so the point is on the line. R is true.
4
After two solutions are known, a third solution moves onto a second line.
Explanation:
False — the third solution is a check of the same line.
5
A tank already holds 10 units of water and gains 2 units each hour. Write y = 2x + 10. Find the water when x = 3. Does the line pass through the origin? 1 unit = 1 litre.
Model answer (board format)
y = 2·3 + 10 = 16 litres. When x = 0, y = 10, not the origin. Because the constant term is 10, the line does not pass through the origin.
Check your answer:
6
Two students found the solutions (3, 5) and (5, 3) of x + y = 8. How can both be right? What happens on the graph?
Model answer (board format)
3 + 5 = 8 and 5 + 3 = 8, so both are solutions. They are two of the infinitely many pairs. Both points lie on the same straight line.
Check your answer:
🏛️ Board exam corner — Bihar Board (BSEB)— CBSE
Switch board with BSEB | CBSE above. The lessons follow the same NCERT chapter.
BSEB model · practiceBoard tip
This page has no verified annual-exam question, because no source page has been added. The model set below is practice in the board pattern.
🏛️ Model questions on one page →
The verified label will be used only when a source page for the question is available.
CBSE-style · competency-based
These are case and assertion-reason practice items. Do not treat them as past CBSE questions.
🔁 Spaced review — today’s questions
Wrong questions return soon; correct ones return after a few days.
🧠 What you learned + equation sheet
What you learned
- In ax + by + c = 0, a and b are not both zero.
- Every solution is an ordered pair, and there are infinitely many such pairs.
- The graph is a straight line. Two points are enough to draw it.
- Every point on the line is a solution. A point off the line is not.
- x = 0 is the y-axis and y = 0 is the x-axis.
- x = a is vertical, y = a is horizontal, and y = mx passes through the origin.
| What | Keep this |
|---|---|
| Standard form | ax + by + c = 0 |
| Solutions | infinitely many pairs |
| Graph | a straight line |
| x = 0 | the y-axis |
| y = 0 | the x-axis |
| y = mx | through the origin |
The notes are original writing. The textbook was used only for activity order and numbers. “Verified” will be used only on a question that has a source page.