## CBSE Class 9 Linear Equations In Two Variables MCQ By Clarify Knowledge

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## CBSE Class 9 Linear Equations In Two Variables MCQ Table

**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 have:**

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.