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 3 of 3 pages

Question 21.

If x = 1, y = 2 is a solution of the equation 3x + 2y = k, the value of k is ___.

Discuss Question

Answer: Option A. ->
:

Putting x = 1, y = 2 in the given equation,
3 x 1 + 2 x 2 = k
$\Rightarrow$ k = 7

Question 22.

If both 'x' and 'y' are natural numbers, the equation 2x + 5y = 7 will have a unique solution.

True
False

Discuss Question

Answer: Option A. -> True
:
A
When

x = 1

2 + 5 y = 7

\Rightarrow

y = 1
When

x = 2

4 + 5 y = 7

\Rightarrow y = \frac{3}{5}

When

x = 3

6 + 5 y = 7

\Rightarrow y = \frac{1}{5}

When

x = 4

8 + 5 y = 7

\Rightarrow y = \frac{- 1}{5}

So, in natural numbers, when x>1, the value of y is <1 and progressively decreases, and then becomes negative at x = 4.
When

y = 2

2 x + 10 = 7

\Rightarrow y = \frac{- 3}{2}

When

y = 3

2 x + 15 = 7

\Rightarrow y = - 4

In natural numbers, when y>1, x<0 and progressively decreases.
Hence, in natural numbers, there is only one pair i.e., (1,1) which satisfy the given equation but in real numbers and rational numbers there are many pairs to satisfy the given linear equation.

Question 23.

x = −5 can be expressed as a linear equation in 2 variables.

True
False

Discuss Question

Answer: Option B. -> False
:
B

A linear equation in two variables is of the form ax + by + c = 0, where a and b are both non-zero. If any one of a or b becomes 0, it would reduce to a linear equation in one variable. So, the equation x = -5 cannot be expressed as a linear equation in 2 variables.

Question 24.

The standard form of a linear equation in two variables x and y, whose respective coefficients are 2 and -3 and has the constant as 4 is ____.

$3 x - 2 y + 4 = 0$
$2 x - 3 y - 4 = 0$
$3 x - 2 y - 4 = 0$
$2 x - 3 y + 4 = 0$

Discuss Question

Answer: Option D. ->

2 x - 3 y + 4 = 0

:
D
The standard form of a linear equation in 2 variables x and y is given by ax + by + c = 0.
It is given that a = 2, b = -3 and c = 4.
Therefore, the linear equation is

2 x - 3 y + 4 = 0

Question 25.

Which of following is a solution of the equation, $2 x + 3 y = 11 ?$

$x = 1, y = 3$
$x = 0, y = 5$
$x = - 2, y = - 5$
$x = 9, y = 1$

Discuss Question

Answer: Option A. ->

x = 1, y = 3

:
A

Substituting each set of the values for $x$ and $y$ in the equation $2 x + 3 y = 11$ , we have
$(i) x = 1, y = 3 L H S = (2 \times 1) + (3 \times 3) = 11 = R H S (i i) x = 0, y = 5 L H S = (2 \times 0) + (3 \times 5) = 15 \neq R H S (i i i) x = - 2, y = - 5 L H S = (2 \times - 2) + (3 \times - 5) = - 19 \neq R H S (i v) x = 9, y = 1 L H S = (2 \times 9) + (3 \times 1) = 21 \neq R H S$
$∴ x = 1, y = 3$ is solution to the given equation.

Question 26.

What will be the linear equation for the given graph?

x=2y
y=2x+5
y=2x+3
2y=x+1

Discuss Question

Answer: Option C. -> y=2x+3
:
C

The coordinates of the points of the graph (0,3) & (-1.5,0) satisfy only the equation y=2x+3:
(0, 3):
3 = 2 x 1 + 3
(-1.5, 0):
0 = 2 $\times$ (-1.5) + 3

Question 27.

If kx - 2ky + 15 = 0 passes through the point (3,-1), then k = -3.

True
False
$x = - 2, y = - 5$
$x = 9, y = 1$

Discuss Question

Answer: Option A. -> True
:
A

Putting x = 3 , y = -1 in the given equation,
k x 3 - 2 x k x -1 + 15 = 0
$\Rightarrow$ 3k + 2k + 15 = 0
$\Rightarrow$ k = -3

Question 28.

The equation $y = m x$ represents ___ ;
where, $(m \neq 0)$ .

a line parallel to x-axis
a line parallel to y-axis
a line passing through the origin
a line cutting x-axis at the point $(m, 0)$

Discuss Question

Answer: Option C. -> a line passing through the origin
:
C
Given equation:

y = m x

Substituting

x = 0

y = m \times 0 = 0

So, if x = 0, then y = 0.
i.e,

(0, 0)

is a point on the line.
Therefore, the line passes through the origin.

Question 29.

Why is a first degree polynomial in two variables ax + by + c = 0, called a linear equation?

It has infinitely many solutions
The geometrical representation is a straight line
It has two variables
None of the above

Discuss Question

Answer: Option B. -> The geometrical representation is a straight line
:
B

The degree (the highest power on any variable) of the given equation is 1. Hence, its geometrical representation is a straight line.

Question 30.

The points (1,0), (-4,0) and (5,0) lie on

X axis
Y axis
a line parallel to the X axis
a line parallel to the Y axis

Discuss Question

Answer: Option A. -> X axis
:
A
We can observe that all the points have zero as their y coordinates.
(1,0), (-4,0) and (5,0)
y = 0 is the equation of X - axis.
Hence, all the points lie on the X axis.