Linear Equations in Two Variables — Class 9 MCQs with Answers

Linear Equations in Two Variables — important questions & MCQs with answers (Class 9 Mathematics)

14 solved questions from this chapter's difficulty levels, each with its answer and explanation. The other 76 are timed and scored when you sign in.

1. Q1Easy

   The standard form of a linear equation in two variables is:

   A.ax + b = 0

   B.ax² + by = 0

   C.ax + by + c = 0✓ Correct

   D.ax + by = c²

   Answer: C. ax + by + c = 0

   Explanation: The standard form places every term on one side: ax + by + c = 0, with a and b not both zero. Confusing this with y = mx + c, which is slope-intercept form, is the usual mix-up.

2. Q2Easy

   Is (2, 3) a solution of 2x + 3y = 13?

   A.Only if x=2

   B.No

   C.Cannot determine

   D.Yes✓ Correct

   Answer: D. Yes

   Explanation: Substitute x=2, y=3 into 2x + 3y: 2(2) + 3(3) = 4 + 9 = 13, matching the right-hand side exactly. A point is a solution only when both sides come out equal after substitution.

3. Q3Easy

   The graph of a linear equation in two variables is always a:

   A.Circle

   B.Parabola

   C.Straight line✓ Correct

   D.Hyperbola

   Answer: C. Straight line

   Explanation: Plotting all solutions of ax + by + c = 0 always traces a straight line, never a curve. Confusing this with y = x² (a parabola) is the usual mix-up.

4. Q4Easy

   Which of the following is a linear equation in two variables?

   A.x² + y = 5

   B.x + y² = 3

   C.2x − 3y = 7✓ Correct

   D.xy = 4

   Answer: C. 2x − 3y = 7

   Explanation: A linear equation in two variables needs both x and y at degree 1, as in 2x − 3y = 7. Terms like x² or xy raise the degree and make an equation non-linear.

5. Q5Easy

   A linear equation in two variables has:

   A.No solution

   B.Infinitely many solutions✓ Correct

   C.Exactly two solutions

   D.Exactly one solution

   Answer: B. Infinitely many solutions

   Explanation: A linear equation in two variables graphs as a straight line, and every point on that line is a solution — infinitely many pairs satisfy it, not just one or two.

6. Q6Easy

   The equation of the x-axis is:

   A.y = 0✓ Correct

   B.x = 0

   C.x = y

   D.x + y = 0

   Answer: A. y = 0

   Explanation: Every point on the x-axis has y-coordinate 0 regardless of x, so the x-axis is the line y = 0. Swapping this with x = 0, which is the y-axis, is the common error.

7. Q7Medium

   A number is 3 more than twice another number y. Express x in terms of y as a linear equation.

   A.2x − y = 3

   B.x = 3y + 2

   C.x + 2y = 3

   D.x = 2y + 3✓ Correct

   Answer: D. x = 2y + 3

   Explanation: '3 more than twice y' means double y, then add 3: x = 2y + 3. Swapping the order to x = 3y + 2 mixes up which number gets doubled and which gets added.

8. Q8Medium

   If (3, k) is a solution of 2x + y = 10, find k.

   A.4✓ Correct

   B.2

   C.−4

   D.6

   Answer: A. 4

   Explanation: Substitute x=3 into 2x+y=10: 2(3)+k=10 → 6+k=10 → k=4. Forgetting to isolate k after substituting leaves the equation half-solved.

9. Q9Medium

   Find the x-intercept of the line 3x + 4y = 12.

   A.12

   B.3

   C.−4

   D.4✓ Correct

   Answer: D. 4

   Explanation: At the x-intercept, y = 0: 3x + 4(0) = 12 gives 3x = 12, so x = 4. Forgetting to set y = 0 first before solving is the common error.

10. Q10Medium

    The temperature conversion C = (5/9)(F − 32). When F = 68, find C.

    A.36

    B.25

    C.20✓ Correct

    D.15

    Answer: C. 20

    Explanation: Substitute F = 68 into C = (5/9)(F − 32): C = (5/9)(68 − 32) = (5/9)(36) = 20°C. Subtracting 32 before multiplying by 5/9, not after, is the key order of steps.

11. Q11Medium

    Write three solutions of x + 2y = 6. Which set is correct?

    A.(0,3),(6,0),(2,2)✓ Correct

    B.(0,6),(3,0),(1,2)

    C.(1,2),(3,1),(6,0)

    D.(0,6),(2,2),(4,1)

    Answer: A. (0,3),(6,0),(2,2)

    Explanation: Check each pair against x + 2y = 6: (0,3) gives 0+6=6, (6,0) gives 6+0=6, and (2,2) gives 2+4=6 — all three satisfy the equation.

12. Q12Hard

    A line passes through (2,5) and has equal x and y intercepts. Find its equation.

    A.x − y = −3

    B.x + y = 7✓ Correct

    C.y = x + 3

    D.x + y = 0

    Answer: B. x + y = 7

    Explanation: Equal x- and y-intercepts means the line has the form x + y = c, since both intercepts equal c in that form. Passing through (2, 5) gives c = 7, so the equation is x + y = 7.

13. Q13Hard

    If the sum of two numbers is 15 and their difference is 3, find the two numbers.

    A.10 and 5

    B.12 and 3

    C.9 and 6✓ Correct

    D.8 and 7

    Answer: C. 9 and 6

    Explanation: Let the numbers be x and y: x + y = 15 and x − y = 3. Adding cancels y, giving 2x = 18, so x = 9 and y = 6.

14. Q14Hard

    The line 2x + 3y = 12 meets the x-axis at A and the y-axis at B. Find the area of triangle OAB.

    A.10

    B.6

    C.8

    D.12✓ Correct

    Answer: D. 12

    Explanation: Find the intercepts of 2x + 3y = 12: y = 0 gives A = (6, 0), and x = 0 gives B = (0, 4). Triangle OAB is right-angled at the origin, so its area is ½ × 6 × 4 = 12 square units.

Linear Equations in Two Variables — FAQs

More Class 9 Mathematics chapters

• 01Orienting Yourself: The Use of Coordinates
• 02Introduction to Linear Polynomials
• 03The World of Numbers
• 04Exploring Algebraic Identities
• 05I'm Up and Down, and Round and Round
• 06Measuring Space: Perimeter and Area

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