### Linear Equations in Two Variables - Test Papers

CBSE Test Paper 01

CH-4 Linear Equations in Two Variables

- For what value of ‘k’, x = 2 and y = -1 is a solution of x + 3y – k = 0?
- 2
- -2
- -1
- 1

- If we divide both sides of a linear equation with a non-zero number, then the solution of the linear equation
- changes
- remains the same
- none of these
- gets divided by the number

- If the line represented by the equation 3x + ky = 9 passes through the points (2, 3), then the value of ‘k’ is
- 2
- 1
- 3
- 4

- How many linear equations in ‘x’ and ‘y’ can be satisfied by x = 2, y = 3?
- only one
- none of these
- many
- two

- The graph of the linear equation y = 3x passes through the point
- (0 , )
- (, 0)
- (0 , )
- (, 2)

- Fill in the blanks:
y + 7 is the equation of a line parallel to _________

- Fill in the blanks:
The equation of X-axis is ________.

If x = 1, y = 2 is a solution of the equation a2x + ay = 3, then find the values of a.

Arvind and Vinod have some erasers. Arvind said to Vinod, if you will give me 10 erasers, I will have twice the erasers left with you. Represent this situation as a linear equation in two variables.

Express the following linear equation in the form ax + by + c = 0 and indicate the values of a, b and c.

5 = 2x

Find whether the given equation have x = 2, y = 1 as a solution:

2x – 3y = 1

If x = 1 and y = 6 is solution of the equation 8x - ay + a2 = 0, find the values of a.

Find four solutions for the following equation: 12x + 5y = 0

Draw the graph of the following linear equation in two variables: 2y = -x + 1.

Draw the graph of the equation 3x + 4y = 12 and find the co-ordinates of the points of intersection of the equation with the co-ordinate axes.

CBSE Test Paper 01

CH-4 Linear Equations in Two Variables

Solution

- (c) -1

Explanation: For finding value of ‘k’, we put x = 2 and y = -1 iin a equation x + 3y – k = 0x+3 y-k=0

2+3(-1)=k

2-3=k

k=-1 - (b) remains the same

Explanation: If then for any non-zero c. We can divide both sides of an equation by a non-zero number c, without changing the equation. - (b) 1

Explanation: If the line represented by the equation 3x + ky = 9 passes through the points (2, 3) then (2,3) will satisy the equation 3x + ky = 93 (2) + 3k = 9

=>6 + 3k = 9

=>3k = 9-6

=>3k = 3

=> k = 1 - (c) many

Explanation: there are infinite many eqution which satisfy the given value x = 2, y = 3

for example

x + y = 5

x - y = -1

3x - 2y = 0

etc.............. - (d) (, 2)
Explanation:

y = 3x

For, y=2, the value of x will be

So (,2)

x-axis

y = 0

It is given that x = 1, y = 2 is a solution of a2x + ay = 3.

a2 1 + a 2 = 3

a2 + 2a - 3 = 0

a2 + 3a - a - 3 = 0

a(a + 3) - 1(a + 3) = 0

(a - 1) (a + 3) = 0

a - 1 = 0 or, a + 3 = 0 a = 1, -3Let number of erasers Arvind have be x

and number of erasers Vinod have be yif Vinod gives 10 erasers to Arvind

Erasers with Arvind = x+10 , Erasers left with Vinod = y-10

A.T.Q. Erasers with Arvind = 2 × Erasers left with Vinod

x+10 = 2(y -10)

x +10 = 2y-20

x - 2y + 30 = 05 = 2x

⇒ –2x + 5 = 0

⇒ –2x + 0.y – 5 = 0

Comparing with ax + by + c = 0, we get

a = –2, b = 0, c = 5For x = 2, y = 1

L.H.S. = 2x – 3y

= 2(2) – 3(1)

= 4 – 3 = 1

= R.H.S.

∴ x = 2, y = 1 is a solution of 2x – 3y = 1.We have,

8x - ay + a2 = 0.....(i)

It is given that x = 1 and y = 6 is a solution of the equation 8x - ay + a2 = 0

On putting the corresponding value of*x*and*y*in (1), we get

8 (1) - a (6) + a2 = 0

8 - 6a + a2 = 0

a2 - 6a + 8 = 0

a2 - 4a - 2a + 8 = 0

a(a - 4) - 2(a - 4) = 0

(a - 4)(a - 2) = 0

a - 4 = 0 or, a - 2 = 0

a = 4 or, a = 2

Hence, a = 4 or, a = 2.12x + 5y = 0

⇒ 5y = –12x

⇒

Put x = 0, then

Put x = 5, then

Put x = 10, then

Put x = 15, then

∴ (0, 0), (5, –12), (10, –24) and (15, –36) are the four solutions of the equation 12x + 5y = 0We have,

2y = -x + 1

y = ......(i)

Putting x = 1 in eq. (i), we get y = = 0

Putting x = -1in eq. (i), we get y = = = 1

Putting x = 3 in eq. (i), we get y = = = -1

Thus, we have the following table represent the equation 2y = -x + 1.x 1 -1 3 y 0 1 -1 Graph of the equation 2y = -x + 1:

3x + 4y = 12

Express y in terms of x.such that it is in the form ofy = mx + c

4y = 12-3x

y = ....(i)

For graph,

Let x = 2, put in (i)

Let x = 4, put in (i)

When line meet x-axis,y = 0When line meet y-axis,x =0

Then 3 (0) + 4y = 12 therefore y = 3

Point of intersection of x-axis is (4, 0).x 2 4 0 y 1.5 0 3 A B C Point of intersection with x-axis is (4, 0) and point of intersection with y-axis is (0,3)