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.
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Exemplar
22 QuestionsThe linear equation 3x – y = x – 1 has
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A unique solution
Two solutions
Infinitely many solutions
No solution
A linear equation in two variables is of the form ax + by + c = 0, where
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a ≠ 0, b ≠ 0
a = 0, b ≠ 0
a ≠ 0, b = 0
a = 0, c = 0
Any point on the y-axis is of the form
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(x, 0)
(x, y)
(0, y)
(y, y)
The linear equation 2x – 5y = 7 has
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A unique solution
Two solutions
Infinitely many solutions
No solution
The equation 2x + 5y = 7 has a unique solution, if x, y are:
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Natural numbers
Positive real numbers
Real numbers
Rational numbers
Any solution of the linear equation 2x + 0y + 9 = 0 in two variables is of the form
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(-9/2, m)
(n, -9/2)
(0, -9/2)
(-9, 0)
The graph of the linear equation 2x + 3y = 6 cuts the y-axis at the point
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(2, 0)
(0, 3)
(3, 0)
(0, 2)
The equation x = 7, in two variables, can be written as
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- x + 1. y = 7
- x + 0. y = 7
- x + 1. y = 7
- x + 0. y = 7
Any point on the x-axis is of the form
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(x, y)
(0, y)
(x, 0)
(x, x)
Any point on the line y = x is of the form
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(a, a)
(0, a)
(a, 0)
(a, –a)
The equation of x-axis is of the form
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x = 0
y = 0
x + y = 0
x = y
The graph of y = 6 is a line
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parallel to x-axis at a distance 6 units from the origin
parallel to y-axis at a distance 6 units from the origin
making an intercept 6 on the x-axis
making an intercept 6 on both the axes
x = 5, y = 2 is a solution of the linear equation
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x + 2y = 7
5x + 2y = 7
x + y = 7
5x + y = 7
If a linear equation has solutions (–2, 2), (0, 0) and (2, –2), then it is of the form
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y – x = 0
x + y = 0
–2x + y = 0
–x + 2y = 0
The positive solutions of the equation ax + by + c = 0 always lie in the
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1st quadrant
2nd quadrant
3rd quadrant
4th quadrant
The graph of the linear equation 2x + 3y = 6 is a line which meets the x-axis at the point
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(0, 2)
(2, 0)
(3, 0)
(0, 3)
The graph of the linear equation y = x passes through the point
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(3/2, -3/2)
(0, 3/2)
(1, 1)
(-1/2, 1/2)
If we multiply or divide both sides of a linear equation with a non-zero number, then the solution of the linear equation:
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Changes
Remains the same
Changes in case of multiplication only
Changes in case of division only
How many linear equations in x and y can be satisfied by x = 1 and y = 2?
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Only one
Two
Infinitely many
Three
The point of the form (a, a) always lies on
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x-axis
y-axis
On the line y = x
On the line x + y = 0
The point of the form (a, – a) always lies on the line
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x = a
y = –a
y = x
x + y = 0