Question 1
1 Mark
The linear equation 3x – y = x – 1 has
Options
Option A
A unique solution
Option B
Two solutions
Option C is correct
Infinitely many solutions
Option D
No solution
Questions & Answers: "Linear Equation in Two Variables"
Complete guide to "Linear Equation in Two Variables" for Math students. Below you will find important questions and model answers to help you prepare.
22 Questions
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Question 2
1 Mark
A linear equation in two variables is of the form ax + by + c = 0, where
Options
Option A is correct
a ≠ 0, b ≠ 0
Option B
a = 0, b ≠ 0
Option C
a ≠ 0, b = 0
Option D
a = 0, c = 0
Question 3
1 Mark
Any point on the y-axis is of the form
Options
Option A
(x, 0)
Option B
(x, y)
Option C is correct
(0, y)
Option D
(y, y)
Question 4
1 Mark
The linear equation 2x – 5y = 7 has
Options
Option A
A unique solution
Option B
Two solutions
Option C is correct
Infinitely many solutions
Option D
No solution
Question 5
1 Mark
The equation 2x + 5y = 7 has a unique solution, if x, y are:
Options
Option A is correct
Natural numbers
Option B
Positive real numbers
Option C
Real numbers
Option D
Rational numbers
Question 6
1 Mark
If (2, 0) is a solution of the linear equation 2x + 3y = k, then the value of k is
Options
Option A is correct
4
Option B
6
Option C
5
Option D
2
Question 7
1 Mark
Any solution of the linear equation 2x + 0y + 9 = 0 in two variables is of the form
Options
Option A is correct
(-9/2, m)
Option B
(n, -9/2)
Option C
(0, -9/2)
Option D
(-9, 0)
Question 8
1 Mark
The graph of the linear equation 2x + 3y = 6 cuts the y-axis at the point
Options
Option A
(2, 0)
Option B
(0, 3)
Option C
(3, 0)
Option D is correct
(0, 2)
Question 9
1 Mark
The equation x = 7, in two variables, can be written as
Options
Option A
- x + 1. y = 7
Option B is correct
- x + 0. y = 7
Option C
- x + 1. y = 7
Option D
- x + 0. y = 7
Question 10
1 Mark
Any point on the x-axis is of the form
Options
Option A
(x, y)
Option B
(0, y)
Option C is correct
(x, 0)
Option D
(x, x)
Question 11
1 Mark
Any point on the line y = x is of the form
Options
Option A is correct
(a, a)
Option B
(0, a)
Option C
(a, 0)
Option D
(a, –a)
Question 12
1 Mark
The equation of x-axis is of the form
Options
Option A
x = 0
Option B is correct
y = 0
Option C
x + y = 0
Option D
x = y
Question 13
1 Mark
The graph of y = 6 is a line
Options
Option A is correct
parallel to x-axis at a distance 6 units from the origin
Option B
parallel to y-axis at a distance 6 units from the origin
Option C
making an intercept 6 on the x-axis
Option D
making an intercept 6 on both the axes
Question 14
1 Mark
x = 5, y = 2 is a solution of the linear equation
Options
Option A
x + 2y = 7
Option B
5x + 2y = 7
Option C is correct
x + y = 7
Option D
5x + y = 7
Question 15
1 Mark
If a linear equation has solutions (–2, 2), (0, 0) and (2, –2), then it is of the form
Options
Option A
y – x = 0
Option B is correct
x + y = 0
Option C
–2x + y = 0
Option D
–x + 2y = 0
Question 16
1 Mark
The positive solutions of the equation ax + by + c = 0 always lie in the
Options
Option A is correct
1st quadrant
Option B
2nd quadrant
Option C
3rd quadrant
Option D
4th quadrant
Question 17
1 Mark
The graph of the linear equation 2x + 3y = 6 is a line which meets the x-axis at the point
Options
Option A
(0, 2)
Option B
(2, 0)
Option C is correct
(3, 0)
Option D
(0, 3)
Question 18
1 Mark
The graph of the linear equation y = x passes through the point
Options
Option A
(3/2, -3/2)
Option B
(0, 3/2)
Option C is correct
(1, 1)
Option D
(-1/2, 1/2)
Question 19
1 Mark
If we multiply or divide both sides of a linear equation with a non-zero number, then the solution of the linear equation:
Options
Option A
Changes
Option B is correct
Remains the same
Option C
Changes in case of multiplication only
Option D
Changes in case of division only
Question 20
1 Mark
How many linear equations in x and y can be satisfied by x = 1 and y = 2?
Options
Option A
Only one
Option B
Two
Option C is correct
Infinitely many
Option D
Three
Question 21
1 Mark
The point of the form (a, a) always lies on
Options
Option A
x-axis
Option B
y-axis
Option C is correct
On the line y = x
Option D
On the line x + y = 0
Question 22
1 Mark
The point of the form (a, – a) always lies on the line
Options
Option A
x = a
Option B
y = –a
Option C
y = x
Option D is correct
x + y = 0