# Class 9 Maths Chapter 4 Linear Equations In Two Variables

**Class 9 Maths Chapter 4 Linear equations in two variables MCQs** are provided here with solutions. The MCQs are prepared as per the latest exam pattern to help students score good marks. These objective questions are provided online with answers and detailed explanations. The chapter-wise MCQs are provided at BYJU’S, as per the latest CBSE syllabus (2021-2022) and NCERT curriculum. Also, check Important Questions for Class 9 Maths here.

## MCQs on Class 9 Maths Chapter 4 Linear Equations in Two Variables

Multiple choice questions for 9th Standard, Linear equations in two variables are given below.

**1) The linear equation 3x-11y=10 has:**

a. Unique solution

b. Two solutions

c. Infinitely many solutions

d. No solutions

Answer:** c**

Explanation: 3x-11y=10

y=(3x-10)/11

Now for infinite values of x, y will also have infinite solutions.

**2) 3x+10 = 0 will has:**

a. Unique solution

b. Two solutions

c. Infinitely many solutions

d. No solutions

Answer:** a**

Explanation: 3x+10 = 0

x = -10/3.

Hence, only one solution is possible.

**3) The solution of equation x-2y = 4 is:**

a. (0,2)

b. (2,0)

c. (4,0)

d. (1,1)

Answer:** c**

Explanation: Putting x=4 and y = 0, on the L.H.S. of the given equation, we get;

4-2(0) = 4 – 0 = 4

Which is equal to R.H.S.

**4) Find the value of k, if x = 1, y = 2 is a solution of the equation 2x + 3y = k.**

a. 5

b. 6

c. 7

d. 8

Answer:** d**

Explanation: 2x + 3y = k

k=2(1)+3(2) = 2+6 = 8

**5) Point (3, 4) lies on the graph of the equation 3y = kx + 7. The value of k is:**

a. 4/3

b. 5/3

c. 3

d. 7/3

Answer:** b**

Explanation: 3y = kx + 7

Here, x = 3 and y = 4

Hence,

(3×4) = (kx3) + 7

12 = 3k+7

3k = 12–7

3k = 5

k = 5/3

**6) The graph of linear equation x+2y = 2, cuts the y-axis at:**

a. (2,0)

b. (0,2)

c. (0,1)

d. (1,1)

Answer:** c**

Explanation: x+2y = 2

y = (2-x)/2

If x=0, then;

y=(2-0)/2 = 2/2 = 1

Hence, x+2y=2 cuts the y-axis at (0,1).

**7) Any point on line x = y is of the form:**

a. (k, -k)

b. (0, k)

c. (k, 0)

d. (k, k)

Answer:** d**

**8) The graph of x = 3 is a line:**

a. Parallel to the x-axis at a distance of 3 units from the origin

b. Parallel to the y-axis at a distance of 3 units from the origin

c. Makes an intercept 3 on the x-axis

d. Makes an intercept 3 on the y-axis

Answer:** b**

**9) In equation, y = mx+c, m is:**

a. Intercept

b. Slope

c. Solution of the equation

d. None of the above

Answer:** b**

**10) If x and y are both positive solutions of equation ax+by+c=0, always lie in the:**

a. First quadrant

b. Second quadrant

c. Third quadrant

d. Fourth quadrant

Answer:** a**

**11) A linear equation in two variables is of the form ax + by + c = 0, where**

(a) a = 0, c = 0

(b) a ≠ 0, b = 0

(c) a = 0, b ≠ 0

(d) a ≠ 0, b ≠ 0

Answer:** d**

Explanation: A linear equation in two variables is of the form ax + by + c = 0, where a ≠ 0, b ≠ 0. If the values of “a” and “b” are equal to 0, the equation becomes c =0. Hence, the values of a and b should not be equal to 0.

**12) Any point on the x-axis is of the form**

(a) (x, y)

(b) (0, y)

(c) (x, 0)

(d) (x, x)

Answer: **c**

Explanation: Any point on the x-axis is of the form (x, 0). On the x-axis, x can take any values, whereas y should be equal to 0.

**13) Any point on the y-axis is of the form**

(a) (y, y)

(b) (0, y)

(c) (x, y)

(d) (x, 0)

Answer: **b**

Explanation: Any point on the y-axis is of the form (0, y). On the y-axis, y can take any values and x should be equal to 0.

**14) The linear equation 2x – 5y = 7 has**

(a) No solution

(b) unique solution

(c) Two solutions

(d) Infinitely many solutions

Answer: **d**

Explanation: The linear equation 2x-5y has infinitely many solutions. Because, the equation 2x-5y = 7 is a single equation, that involves two variables. Hence, for different values of x, we will get different values of y and vice-versa.

**15) The linear equation 3x – y = x – 1 has**

(a) No solution

(b) unique solution

(c) Two solutions

(d) Infinitely many solutions

Answer: **d**

Explanation: The linear equation 3x – y = x – 1 has infinitely many solutions.

On simplification, the given equation becomes 2x-y= -1, which is a single equation with two variables. Thus, 3x – y = x – 1 has infinitely many solutions.

**16) The graph of the linear equation 2x + 3y = 6 cuts the y-axis at the point**

(a) (2, 0)

(b) (0, 2)

(c) (3, 0)

(d) (0, 3)

Answer: **b**

Explanation:

Given that the graph of the linear equation 2x + 3y = 6 cuts the y-axis at the point. Let the point be “P”. Hence, the x -coordinate of point P is 0.

Now, substitute x= 0 in the given equation,

2(0) + 3y = 6

3y = 6

y=2

Hence, the cooridnate point is (0, 2).

**17) The equation 2x + 5y = 7 has a unique solution, if x, y are:**

(a) Rational numbers

(b) Real numbers

(c) Natural numbers

(d) Positive real numbers

Answer: **c**

Explanation: The equation 2x + 5y = 7 has a unique solution, if x, y are natural numbers.

In natural numbers, there exists only one pair (1, 1) which satisfies the given equation. But for rational numbers, real numbers, positive real numbers, there exist many solution pairs to satisfy the equation.

**18) The point of the form (a, a) always lies on:**

(a) On the line x + y = 0

(b) On the line y = x

(c) x-axis

(d) y-axis

Answer: **b**

Explanation: The point of the form (a, a) always lies on the line y = x. If the point has the same x and y values, it should lie on the same line.

**19) If we multiply or divide both sides of a linear equation with the same non-zero number, then the solution of the linear equation:**

(a) Remains the same

(b) Changes

(c) Changes in case of multiplication only

(d) Changes in case of division only

Answer: **a**

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

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

(a) 2

(b) 4

(c) 5

(d) 6

Answer: **b**

Explanation:

Substitute x=2 and y=0 in the given equation, we get

2(2) + 3(0) = k

k = 4+0

k = 4.

Hence, the value of k is 4.

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