Mock Test - Linear Equations in Two Variables

Class 9 Mathematics – Chapter 4: Linear Equations in Two Variables (MCQ Mock Test)

Strengthen Your Algebra Skills with the Linear Equations MCQ Mock Test!

Can you represent equations graphically or find their solutions easily? Test your understanding with this MCQ-based mock test on Linear Equations in Two Variables, designed as per the latest Class 9 Maths syllabus. This test includes all important concepts — standard form of linear equations, plotting their graphs, finding solutions, and interpreting parallel and intersecting lines.

Each question helps you apply mathematical reasoning, enhance visualization skills, and gain confidence for exams. Whether you’re preparing for school tests or revising for finals, this mock test is the perfect way to build a strong foundation for algebra and coordinate geometry.

Attempt now and make solving Linear Equations in Two Variables simpler than ever!

1. If we multiply or divide both sides of a linear equation with a non-zero number, then the solution of the linear equation:

changes

remains the same

changes in case of multiplication only

changes in case of division only.

2. Assertion (A): x = 4 is a line parallel to x-axis.
Reason (R): The equation of the line parallel to the y-axis is x = a.

Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).

Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).

Assertion (A) is true but reason (R) is false.

Assertion (A) is false but reason (R) is true.

3. Assertion (A): A linear equation 3x + 5y =2 has infinitely many solutions.
Reason (R): A linear equation in two variables has many infinitely solutions.

Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).

Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).

Assertion (A) is true but reason (R) is false.

Assertion (A) is false but reason (R) is true.

4. A linear equation in two variables is of the form ax + by + c = 0, where

a ≠ 0, b ≠ 0

a = 0, b ≠ 0

a ≠ 0, b = 0

a = 0, c = 0

5. At what point the graph of the linear equation 2x + 5y = 10 cuts the y-axis?

(0,1)

(0,2)

(0,3)

(0,4)

6. The equation of x-axis is of the form

x = 0

y = 0

x + y = 0

x = y

7. The graph of x = ± a is a straight line parallel to the

x-axis

y-axis

line y = x

line x + y = 0

8. How many solution(s) of the linear equation 2x + 3y = 18 has?

One

Two

Infinite

Three

9. Side of an equilateral triangle is x. If the perimeter is 30 cm, find the value of x.

10. For one of the solutions of the equation ax + by + c = 0, x is negative and y is positive then surely a portion of line lies in the

first quadrant

second quadrant

third quadrant

fourth quadrant

11. For what value of k, x = 2 and y = –1 is a solution of x + 3y – k = 0.

-1

12. x = 5, y = –2 is a solution of the linear equation

2x + y = 9

2x – y = 12

x + 3y = 1

x + 3y = 0

13. The equation 2x + 5y = 7 has a unique solution, if x, y are

Natural numbers

Positive real numbers

Real numbers

Rational numbers

14. The equation x = 5 in two variables can be written as

1.x + 1.y = 5

0.x + 1.y = 5

0.x + 0.y = 5

1.x + 0.y = 5

15. Any point on the line y = x is of the form

(a, a)

(0, a)

(a, 0)

(a, – a)

16. The graph of the linear equation y = 2x passes through the point

(2, 1)

(2, – 1)

17. If the linear equation has solutions (– 3, 3), (0, 0), (3, – 3), then equation is

x – y = 0

x + y = 0

2x – y = 0

x + 2y = 0

18. The solution of the linear equation x + 2y = 8 which represents a point on x-axis is (0, 4).

True

False

19. Assertion (A): x + y = 6 is the equation of a line passing through the origin.
Reason (R): y = mx is the equation of a line passing through the origin.

Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).

Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).

Assertion (A) is true but reason (R) is false.

Assertion (A) is false but reason (R) is true.

20. If point (3, 0) lies on the graph of the equation 2x + 3y = k, then the value of k is

21. Assertion (A): There are infinite number of lines passing through (2, 5).
Reason (R): A linear equation in two variables has unique solution.

Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).

Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).

Assertion (A) is true but reason (R) is false.

Assertion (A) is false but reason (R) is true.

22. Any solution of the linear equation 2x + 0y = 9 in two variables, is of the form

(a)

(b)

(c)

(d)

23. The equation x = 5 in two variables can be written as

1.x + 1.y = 5

0.x + 1.y = 5

0.x + 0.y = 5

1.x + 0.y = 5

24. Find b, if linear equation 3bx – y = 9 has one solution as (3, 3).

1/3

2/3

4/3

Zero

25.

If (2, 0) is a solution of the linear equation 2x + 3y = k, then find the value of k.

26. How many linear equations in x and y can be satisfied by x = 1 and y = 2?

Only one

Two

Infinitely many

Three

27. Find the value of b, if x = 5, y = 0 is a solution of the equation 3x + 5y = b.

28. Let y varies directly as x. If y = 24, when x = 8, then the linear equation is

3y = x

y = x

y = 4x

y = 3x

29. The linear equation 3y – 5 = 0, represented as ax + by + c = 0, h

a unique solution

infinitely many solutions

two solutions

no solution

30. The graph of the linear equation 3x + 5y = 15 cuts the x-axis at the point

(5, 0)

(3, 0)

(0, 5)

(0, 3)

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