Linear Equations In Two Variables(9th Grade > Mathematics ) Questions and answers for exam Preparation

9th Grade > Mathematics

LINEAR EQUATIONS IN TWO VARIABLES MCQs

Total Questions : 30 | Page 2 of 3 pages

Question 11.

The geometrical representation of a linear equation is a

Straight line
curve
circle
parabola

Discuss Question

Answer: Option A. -> Straight line
:
A

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

Question 12.

A linear equation in two variables

Has no solution
Has one solution
Has two solutions
Has infinitely many solutions

Discuss Question

Answer: Option D. -> Has infinitely many solutions
:
D

A linear equation in two variables is of the form $x + b y + c = 0$
$\Rightarrow x = - c - b y$
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 13.

Select the equation whose graph is given alongside:

y = 2x + 2
3y = 6x - 15
y - 2x = 4
y = 2x - 4

Discuss Question

Answer: Option D. -> y = 2x - 4
:
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.

Question 14.

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

(0, 16)
(4, 0)
(0, 8)
(3, 2)

Discuss Question

Answer: Option A. -> (0, 16)
:
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 $\times$ 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 $\times$ 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:
$4 (0) + 8 = 8 \neq 16 (R H S)$ , 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 $4 (3) + 2 = 14 \neq 16 (R H S)$ , and thus (3, 2) is also not a soltuion of the given equation.

Question 15.

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

Discuss Question

Answer: Option D. -> 22
:
D
If

a = - 1, b = 4

is the solution of equation

- 2 a = - 5 b + k

, then they will satisfy the given equation.
Putting values of

a & b

in the given equation.
So,

- 2 (- 1) = - 5 (4) + k 2 = - 20 + k \Rightarrow k = 20 + 2 \Rightarrow k = 22

.
Therefore, the value of k is 22.

Question 16.

Co-ordinates of P and Q are _______ respectively:

(1, 1) & (2, 0)
(1, 1) & (0, 2)
(1, 2) & (0, 1)
(2, 0) & (1,2)

Discuss Question

Answer: Option B. -> (1, 1) & (0, 2)
:
B

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

Question 17.

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)

x - 3y = 0
2x + 1 = y
x + 3y = 0
3x - y = 0

Discuss Question

Answer: Option A. -> x - 3y = 0
:
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 18.

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)

4 units
3 units
5 units
None of these

Discuss Question

Answer: Option C. -> 5 units
:
C

4 x + 3 y = 12 P u t y = 0 t h e n, w e g e t 4 x + 3 (0) = 12 \Rightarrow x = 3 ∴ A (3, 0) c u t s t h e x - a x i s P u t x = 0 t h e n, w e g e t 4 (0) + 3 y = 12 \Rightarrow y = 4 ∴ B (0, 4) c u t s t h e y - a x i s

If The Graph Of The Equation 4x + 3y = 12 cuts The Coordina...

I n △ A O B, AB is the hypotenuse of the given triangle. T h e l e n g t h O A = 3 u n i t s a n d O B = 4 u n i t s B y p y t h o g o r a s t h e o r e m, A B = \sqrt{O A^{2} + O B^{2}} = \sqrt{3^{2} + 4^{2}} = \sqrt{25} = 5 u n i t s

Question 19.

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

True
False
5 units
None of these

Discuss Question

Answer: Option A. -> True
:
A

x + y = 0
$\Rightarrow$ 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 20.

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

Discuss Question

Answer: Option A. -> True
:

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.