# Free Linear Equations in Two Variables 02 Practice Test - 9th Grade

The geometrical representation of a linear equation is a

A.

Straight line

B.

curve

C.

circle

D.

parabola

#### SOLUTION

Solution : A

A linear relation between two variables is geometrically represented by a straight line on the Cartesian plane.

A linear equation in two variables

A.

Has no solution

B.

Has one solution

C.

Has two solutions

D.

Has infinitely many solutions

#### SOLUTION

Solution : D

A linear equation in two variables is of the form x+by+c=0
x=cby
For every unique value of x, we get a unique value of y satisfying the above equation. Therefore, a linear equation in two variables can have infinitely many solutions.

Select the equation whose graph is given alongside: A.

y = 2x + 2

B.

3y = 6x - 15

C.

y - 2x = 4

D.

y = 2x - 4

#### SOLUTION

Solution : D

By looking at the graph we can easily say that the line passes through the points (2,0) and (0,-4).

We can identify which line passes through these points by substituting the points in the equation of the line.

Plugging x = 2, y = 0 in equation y = 2x - 4, we get

0 = 2(2) - 4 = 0

Plugging x = 0, y = -4 in equation y = 2x - 4, we get

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

The equation y = 2x - 4 is satisfied by both the points. So, given graph belongs to y = 2x - 4.

Identify the solutions for the given equation 4x + y = 16.

A.

(0, 16)

B.

(4, 0)

C.

(0, 8)

D.

(3, 2)

#### SOLUTION

Solution : A and B

The given equation is 4x + y = 16.

(i) (0, 16)
Putting x = 0 and y = 16 in the given equation:
LHS = (4 × 0) + 16 = 16 (RHS)
Thus, (0, 16) is a solution of the given equation.

(ii) (4, 0)
Putting x = 4 and y = 0 in the given equation:
LHS = (4 × 4) + 0 = 16 (RHS)
Thus, (4, 0) is a solution of the given equation.

(iii) (0, 8)
If we put x = 0 and y = 8 in the given equation:
4(0)+8=816(RHS), and thus (0, 8) is not a soltuion of the given equation.

(iv) (3, 2)
Similarly, putting x = 3 and y = 2 in the given equation, we get 4(3)+2=1416(RHS), and thus (3, 2) is also not a soltuion of the given equation.

Find the value of k, when a=1 and b=4 is the solution of the equation 2a=5b+k.

A. 34
B. -18
C. 20
D. 22

#### SOLUTION

Solution : D

If a=1,b=4 is the solution of equation 2a=5b+k, then they will satisfy the given equation.

Putting values of a & b in the given equation.
So,
2(1)=5(4)+k2=20+kk=20+2k=22.

Therefore, the value of k is 22.

Co-ordinates of P and Q are _______ respectively: A.

(1, 1) & (2, 0)

B.

(1, 1) & (0, 2)

C.

(1, 2) & (0, 1)

D.

(2, 0) & (1,2)

#### SOLUTION

Solution : B Coordinate P is (1, 1) and Q is (0, 2)

The price of 1 kg oranges is thrice the price of 1 kg apples. Which of the following linear equation represents the given statement ?
(Assume the the price of 1 kg oranges to be x and of 1 kg apples to be y)

A. x - 3y = 0
B. 2x + 1 = y
C. x + 3y = 0
D. 3x - y = 0

#### SOLUTION

Solution : A

Given, the price of 1 kg of oranges is x and that of 1 kg of apples is y.

According to the given condition, the price of the 1 kg oranges is three times the price of the 1 kg apple.
So, x = 3y.
Therefore, x - 3y = 0

If the graph of the equation 4x + 3y = 12 cuts the coordinate axes at A and B, then hypotenuse of right angle triangle AOB is of length ___. (O is origin)

A. 4 units
B. 3 units
C. 5 units
D. None of these

#### SOLUTION

Solution : C

4x+3y=12Put y=0 then,we get4x+3(0)=12x=3A(3,0) cuts the xaxisPut x=0 then, we get4(0)+3y=12y=4B(0,4) cuts the yaxis In AOB,AB is the hypotenuse of the given triangle.The length OA=3 units and OB=4 unitsBy pythogoras theorem,AB=OA2+OB2      =32+42=25=5 units

A point on the line x + y = 0 can be represented as (a,-a).

A.

True

B.

False

#### SOLUTION

Solution : A

x + y = 0
x = - y or y = - x

If x = a, y = -a

Any point on the line x + y = 0 can be represented as (a,-a)

The straight line x = a (where a is a constant) is parallel to the ___ - axis.

#### SOLUTION

Solution : Any straight line that is parallel to the Y-axis will always pass through one constant point on the X-axis. Hence, all the straight lines that are parallel to the Y-axis can be represented as x = a.