# Free Linear Equations in Two Variables 03 Practice Test - 9th Grade

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

#### SOLUTION

Solution :

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

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

A.

True

B.

False

#### SOLUTION

Solution : 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.

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

A. True
B. False

#### SOLUTION

Solution : A

When x=1,
2+5y=7
y = 1

When x=2,
4+5y=7
y=35

When x=3,
6+5y=7
y=15

When x=4,
8+5y=7
y=15

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,
2x+10=7
y=32

When y=3,
2x+15=7
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.

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 ____.

A. 3x2y+4=0
B. 2x3y4=0
C. 3x2y4=0
D. 2x3y+4=0

#### SOLUTION

Solution : 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 2x3y+4=0

What will be the linear equation for the given graph? A.

x=2y

B.

y=2x+5

C.

y=2x+3

D.

2y=x+1

#### SOLUTION

Solution : 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 × (-1.5) + 3

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

A.

x=1, y=3

B.

x=0, y=5

C.

x=2, y=5

D.

x=9, y=1

#### SOLUTION

Solution : A

Substituting each set of the values for x and y in the equation 2x+3y=11, we have

(i) x=1, y=3LHS=(2×1)+(3×3)=11=RHS (ii) x=0, y=5LHS=(2×0)+(3×5)=15RHS (iii) x=2, y=5LHS=(2×2)+(3×5)=19RHS (iv) x=9, y=1LHS=(2×9)+(3×1)=21RHS

x=1, y=3 is solution to the given equation.

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

A.

True

B.

False

#### SOLUTION

Solution : A

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

The equation y=mx represents ___ ;
where, (m0).

A. a line parallel to x-axis
B. a line parallel to y-axis
C. a line passing through the origin
D.  a line cutting x-axis at the point (m,0)

#### SOLUTION

Solution : C

Given equation: y=mx
Substituting x=0,
y=m×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.

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

A.

It has infinitely many solutions

B.

The geometrical representation is a straight line

C.

It has two variables

D.

None of the above

#### SOLUTION

Solution : B

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

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

A. X axis
B.  Y axis
C. a line parallel to the X axis
D. a line parallel to the Y axis

#### SOLUTION

Solution : 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.