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This mock test of Test: Solutions To Linear Equations for Class 9 helps you for every Class 9 entrance exam.
This contains 19 Multiple Choice Questions for Class 9 Test: Solutions To Linear Equations (mcq) to study with solutions a complete question bank.
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QUESTION: 1

The positive solution of equation ax + by + c = 0 always lie in the:

Solution:

The solution of the linear equation is represented by the ordered pair (x,y)

Hence if x>0 , y>0 , then the solution will always lie in the first quadrant.

QUESTION: 2

For two lines 2x + y = 1 and x – y = 2 if the x coordinate of the common point is 1 what is the y coordinate?

Solution:

QUESTION: 3

Which of the following points lies on the line 3x + 2y = 6?

Solution:

Put the given points in the equation 3x + 2y = 6

If L.H.S of the equation is equal to R.H.S

then the given points will lie on the line

3x + 2y = 6

3.0 + 2.3 = 6

6 =6

L.H.S = R.H.S

So the given point lie on the line.

QUESTION: 4

Rozly can row downstream 20km in 2 hours, and the upstream 4km in 2 hours. What will be the speed of rowing in still water?

Solution:

Upstream = (x-y) km/hr

Downstream =(x+y)km/hr

20(x+y)=2

X+Y=10.....(1)

4(x-y)=2

x-y=2....(2)

Solve both equations

x+y=10

x-y=2

2x=12

X=6

Substitute x=6in i

6+y=10

Y=4

Speed of rowing in still water is 4km/hr.

So option B is correct answer.

QUESTION: 5

The linear equation 2x + 5y = 8 has:

Solution:

QUESTION: 6

The value of m, if a = 3 and b = 1 is the solution of equation 2a + 3b = m is:

Solution:

In the given question we have a=3,b=1 the given equation is 2a + 3b=m

By substituting the values of a,b in the given equation, we get ,

2 x 3 + 3 x 1 = m

6 + 3 = m

9 = m

So option A is the correct answer.

QUESTION: 7

Which of the following is the solution of linear equation

Solution:

QUESTION: 8

All linear equations in two variables have ————– .

Solution:

QUESTION: 9

The value of k if x = 2, y = 1 is a solution of equation 2x – k = – 3y is:

Solution:

If x = 2, y = 1 is a solution of the equation 2x + 3y = k, then these values will satisfy the equation. So, putting x = 2 and y = 1 in the equation, we get

2(2) + 3(1) = k

⇒ 4 + 3 = k

⇒ k = 7.

QUESTION: 10

If -0.25x + 1.3 = -0.55x – 0.2, then x

Solution:

Given equation is :

-0.25x + 1.3 = -0.55x – 0.2

-0.25x + 0.55x = -0.2 - 1.3

0.30 x = -1.5

So x = -1.5 / 0.30

x = -5

So option B is correct answer.

QUESTION: 11

The point lying on the equation 2x – y = 5 is:

Solution:

The point will lie on the line if L.H.S of the equation is equal to R.H.S

Given equation is 2x - y = 5

Put the point ( 2 , -1) in the above equation

2 . 2 - (-1) = 4 + 1 = 5 = R.H.S

So this proves that the given points lie on the line.

So option D is correct answer.

QUESTION: 12

The value of k if x = 2, y = 1 is a solution of equation 2x – k = – 3y is

Solution:
2*2-k=-3*1(by putting the value of X and y)

4-k=-3

4+3=k

k=7

4-k=-3

4+3=k

k=7

QUESTION: 13

Point P(2,-3) lies on the line represented by the equation:

Solution:

QUESTION: 14

Find value of a and b if y = 1 and x = 2 is solution of linear equation ax + by = 3 and 3a – 2b = 1

Solution:

Given Equations

ax + by = 3 {1}

3a - 2b = 1 {2}

x = 2, y = 1 ( given)

Equation {1} becomes,

2a + b = 3 {3}

Substract equation {3} from {2}, we get,

2a + b - 3a + 2b = 3 - 1

-a + 3b = 2

3b = 2 + a

b = (2+a) / 3

Put the value of b in equation {3}, we get

2a + (2 +a ) / 3 = 3

(6a +a +2) / 3 = 3

7a + 2 = 9

a = 1

Now put value of a in {3}

2 + b = 3

b = 1

hence we get value of a and b i.e. 1 and 1

QUESTION: 15

Which of the following is a solution of the equation 4x + 3y = 16?

Solution:

Given equation is :

4x + 3y = 16

Putting x = 1 and y = 4

4 .1 + 3. 4 = 16

4 + 12 = 16

16 = 16

So option D is the correct answer.

QUESTION: 16

Solutions of the equation 2x + 5y = 0 is:

Solution:

QUESTION: 17

(2,-3) is a solution of 3x + 4y + k = 0. So, the value of k must be

Solution:

QUESTION: 18

If the line represented by the equation 3x + αy = 8 passes through the points (2,2), then the value of α is

Solution:

Given that the equation 3x + ay = 8 passes through the point (2,2) it means that (2,2) is a solution of the equation

Putting X= 2 and Y = 2 in the equation we have

3(2) + a (2) = 8

6 + 2a = 8

2a = 8-6

2a = 2

a = 2/2 = 1

Therefore value of

a = 1

So option D is correct answer.

QUESTION: 19

The number of lines passing through (3, 4) are

Solution:

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