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

### Question 1

The geometrical representation of a linear equation is a

Straight line

curve

circle

parabola

#### SOLUTION

Solution :A

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

### Question 2

A linear equation in two variables

Has no solution

Has one solution

Has two solutions

Has infinitely many solutions

#### SOLUTION

Solution :D

A linear equation in two variables is of the form x+by+c=0

⇒x=−c−by

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.

### Question 3

Select the equation whose graph is given alongside:

y = 2x + 2

3y = 6x - 15

y - 2x = 4

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 get0 = 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.

### Question 4

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

(0, 16)

(4, 0)

(0, 8)

(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=8≠16(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=14≠16(RHS), and thus (3, 2) is also not a soltuion of the given equation.

### Question 5

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

#### 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+k⇒k=20+2⇒k=22.

Therefore, the value of k is 22.

### Question 6

Co-ordinates of P and Q are _______ respectively:

(1, 1) & (2, 0)

(1, 1) & (0, 2)

(1, 2) & (0, 1)

(2, 0) & (1,2)

#### SOLUTION

Solution :B

Coordinate P is (1, 1) and Q is (0, 2)

### Question 7

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)

#### 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

### Question 8

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)

#### SOLUTION

Solution :C

4x+3y=12Put y=0 then,we get4x+3(0)=12⇒x=3∴A(3,0) cuts the x−axisPut x=0 then, we get4(0)+3y=12⇒y=4∴B(0,4) cuts the y−axis

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

### Question 9

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

True

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)

### Question 10

The straight line x = a (where a is a constant) is parallel to the

#### 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.