# Free Linear Equations in Two Variables 01 Practice Test - 9th Grade

Which of the following equations have x=4 and y=2 as a solution?

A.

2x+3y=12

B.

4x+y=19

C.

x+y=6

D.

3x+2y=15

#### SOLUTION

Solution : C

Putting x=4 and y=2 in each of the given equations, we get the following:

2x+3y=12:
LHS =2×4+3×2=14 RHS

4x+y=19:
LHS =4×4+2=18 RHS

x+y=6:
LHS =4+2=6= RHS

3x+2y=15:
LHS =3×4+2×2=16 RHS

Hence, x=4,y=2 is a solution of the equation x+y=6.

If y = 4x is written in the form of ax + by + c = 0, then which of the following options represents the values of a, b and c respectively?

A.

-4, 1, 0

B.

4, 1, 0

C.

4, 0, 1

D.

1, -4, 0

#### SOLUTION

Solution : A

y = 4x can be rewritten as -4x + y = 0.

On comparing 4x - y = 0 with
ax + by + c = 0, we get
a = -4
b = 1
c = 0

4, -1, 0 are the values of a, b and c respectively.

Which of the following statements are true about the graph of the line x + 2y = 0.

A. is parallel to the x-axis
B. is parallel to the Y axis
C. passes through the origin
D. (0,3) lies on the line

#### SOLUTION

Solution : C

If x = 0,
0 + 2y = 0
y = 0
The line x + 2y = 0 passes through the origin.

We know that for x + 2y = 0 ,
y = 0 when x = 0.
Therefore, (0,3) does not lie on the line.

How would you rewrite 2y = 3 in the standard form ax + by + c = 0 ?

A. 0x + 2y - 3 = 0
B. 0x + 2y = -3
C. 0x + 2y + 3 = 0
D. 0x - 2y -3 = 0

#### SOLUTION

Solution : A

The standard form is given by ax + by + c = 0
So, 2y = 3 can be written in the form 0x + 2y - 3 = 0.

The graph of the linear equation 3x - 2y = 6 cuts the y-axis at the point (0,3).

A.

True

B.

False

#### SOLUTION

Solution : B

At the y-axis, value of x = 0

Putting x = 0 in the given equation,

3 x 0 - 2y = 6

y = -3.

Hence, the line 3x - 2y = 6 cuts y-axis at the point (0,-3).

Identify the points which lie on the line 3x+4y=7.

A.

(1,1)

B.

(0,74)

C.

(0,7)

D.

(73,0)

#### SOLUTION

Solution : A, B, and D

If a point lies on a line, the coordinates should satisfy the equation of the line.
So, any point lying on the line 3x + 4y = 7 is a solution of the equation.

Let's substitute the points given in the options in 3x + 4y = 7 to check which of them satisfy the equation.

(1,1):
LHS=3x+4y=3×(1)+4×(1)                            =7=RHS

(0,74):
LHS=3x+4y=3×(0)+4×(74)                            =7=RHS

(0,7):
LHS=3x+4y=3×(0)+4×(7)                           =28RHS

(73,0):
LHS=3x+4y=7=3×(73)+4×(0)                            =7=RHS

Points (1,1), (0,74) and (73,0) lie on the given line.

The line x + y = 3 lies closer to the origin as compared to the line x + y = 5 when plotted on the cartesian plane.

A.

True

B.

False

#### SOLUTION

Solution : A

Let us consider the equation x + y = 3
when x = 0 then y = 3
similarly, when y = 0 then x = 3

Let us consider the equation x + y = 5
when x = 0 then y = 5
similarly, when y = 0 then x = 5

By plotting the graphs of both of the equations, we can easily observe that the line x + y = 3 lies closer to the origin.

The solution of a linear equation is not affected when

A.

The same numbers are added to both sides of the equation

B.

We multiply or divide both the sides of the equation by the same non-zero numbers

C.

We add a number to one side and subtract the same number from the other side of the equation

D.

We multiply one side with a number and divide the same number from the other side of the equation

#### SOLUTION

Solution : A and B

The solution of the equation remains unchanged if the same numbers are added to both sides of the equation.
Also, when we multiply or divide both the sides of the equation by the same non-zero number, the solution remains unchanged.

For example, in the equation x + 2y = 3, if we add 4 to both sides of the equation, the new equation will be x + 2y + 4 = 7. The values of x and y that satisfies the original equation will satisfy the new equation obtained as well.

The distance between the lines x = -3 and x = 2 is _____.

A. 5 units
B. 3 units
C. 2 units
D. 1 units

#### SOLUTION

Solution : A

Both the lines are parallel to y-axis.

The line x = -3 lies at a distance of 3 units to the left side of the origin and the line x = 2 lies at a distance of 2 units to the right side of the origin.

Therefore, the distance between the lines is (3 + 2) units or 5 units.

If the point (3, 5) lies on the graph of the equation 3y = ax + 9, the value of a is

___

.

#### SOLUTION

Solution :

If the point lies on the graph then it satisfies the given equation,
Putting x = 3, y = 5 in the given equation,
3×5=a×3+9
3a + 9 = 15
a = 2