Pair of Linear Equations in Two Variables: Most Important 50 MCQs

Pair of Linear Equations in Two Variables

A pair of linear equations in two variables can be represented as:
a)
$ax^2 + by + c = 0$
b)
$ax + by + c = 0$
c)
$ax^3 + by^2 + c = 0$
d) None of these
Answer: b
The graphical representation of a pair of linear equations is:
a) Two straight lines
b) Two curves
c) A parabola and a straight line
d) A single point
Answer: a
If two lines intersect at a single point, the equations are:
a) Inconsistent
b) Consistent with a unique solution
c) Consistent with infinitely many solutions
d) None of these
Answer: b
If two lines are parallel, the pair of equations is:
a) Consistent
b) Inconsistent
c) Dependent
d) None of these
Answer: b
The condition for two lines to be coincident is:
a)
$\frac{a_1}{a_2} \neq \frac{b_1}{b_2}$
b)
$\frac{a_1}{a_2} = \frac{b_1}{b_2} \neq \frac{c_1}{c_2}$
c)
$\frac{a_1}{a_2} = \frac{b_1}{b_2} = \frac{c_1}{c_2}$
d) None of these
Answer: c
The substitution method involves:
a) Adding the equations
b) Multiplying the equations
c) Expressing one variable in terms of another
d) None of these
Answer: c
A consistent pair of equations may have:
a) No solution
b) A unique solution
c) Infinitely many solutions
d) Both b and c
Answer: d
If two equations are
$x – y = 2$
and
$3x – 3y = 6$
, then the lines are:
a) Parallel
b) Intersecting
c) Coincident
d) None of these
Answer: c
The elimination method involves:
a) Eliminating one variable
b) Eliminating both variables
c) Adding constants
d) Multiplying variables
Answer: a
If the pair of equations
$2x + 3y = 6$
and
$4x + 6y = 12$
is given, the lines are:
a) Intersecting
b) Parallel
c) Coincident
d) None of these
Answer: c
The general form of a pair of linear equations is:
a)
$a_1x^2 + b_1y + c_1 = 0$
b)
$a_1x + b_1y + c_1 = 0$
and
$a_2x + b_2y + c_2 = 0$
c)
$a_1x + b_1y + c_1 = 0$
and
$a_2x^2 + b_2y + c_2 = 0$
d) None of these
Answer: b
If
$5x – 3y = 2$
and
$3x – 2y = 1$
, then the pair of equations has:
a) No solution
b) Unique solution
c) Infinitely many solutions
d) None of these
Answer: b
The graphical solution of a pair of linear equations is the:
a) Point of intersection of the lines
b) Parallel distance between the lines
c) Slope of one of the lines
d) None of these
Answer: a
The condition for two lines to be parallel is:
a)
$\frac{a_1}{a_2} \neq \frac{b_1}{b_2}$
b)
$\frac{a_1}{a_2} = \frac{b_1}{b_2} \neq \frac{c_1}{c_2}$
c)
$\frac{a_1}{a_2} = \frac{b_1}{b_2} = \frac{c_1}{c_2}$
d) None of these
Answer: b
In the elimination method, after eliminating one variable, the resulting equation is in:
a) One variable
b) Two variables
c) Three variables
d) None of these
Answer: a
The solution of the pair of equations
$x + y = 5$
and
$x – y = 1$
is:
a)
$x = 3, y = 2$
b)
$x = 2, y = 3$
c)
$x = -1, y = -2$
d) None of these
Answer: a
The cost of 5 pencils and 7 pens is ₹50, and the cost of 7 pencils and 5 pens is ₹46. What is the cost of a pen?
a) ₹3
b) ₹4
c) ₹5
d) ₹6
Answer: a
For the pair of equations
$2x + 3y = 5$
and
$4x + 6y = 10$
, the solution is:
a) Unique
b) No solution
c) Infinitely many solutions
d) None of these
Answer: c
If two linear equations have infinitely many solutions, the lines:
a) Intersect at one point
b) Are parallel
c) Coincide
d) None of these
Answer: c
If the pair of equations
$x + 2y = 6$
and
$2x + 4y = 12$
is solved graphically, the lines are:
a) Parallel
b) Intersecting
c) Coincident
d) None of these
Answer: c
The solution of the pair of equations
$x + y = 7$
and
$x – y = 3$
is:
a)
$x = 5, y = 2$

b)
$x = 4, y = 3$

c)
$x = 6, y = 1$

d) None of these
Answer: a
The condition for a pair of linear equations to have no solution is:
a)
$\frac{a_1}{a_2} \neq \frac{b_1}{b_2}$

b)
$\frac{a_1}{a_2} = \frac{b_1}{b_2} \neq \frac{c_1}{c_2}$

c)
$\frac{a_1}{a_2} = \frac{b_1}{b_2} = \frac{c_1}{c_2}$

d) None of these
Answer: b
If two lines are represented by the equations
$3x + 4y = 7$
and
$6x + 8y = 14$
the lines are:
a) Parallel
b) Intersecting
c) Coincident
d) None of these
Answer: c
A pair of linear equations has no solution when:
a) The lines intersect
b) The lines coincide
c) The lines are parallel
d) None of these
Answer: c
If
$x = 2, y = 3$
is a solution of the equation
$ax + by = 12$
then
$a + b$
is:
a) 5
b) 6
c) 7
d) 4
Answer: a
The pair of equations
$x + y = 10$
and
$2x + 2y = 20$
has:
a) No solution
b) Infinitely many solutions
c) A unique solution
d) None of these
Answer: b
The graphical representation of the equations
$x + y = 4$
and
$x – y = 2$
will show:
a) Parallel lines
b) Intersecting lines
c) Coincident lines
d) None of these
Answer: b
If
$x = 0$
and
$y = -1$
satisfies
$ax + by = -1$
the value of b is:
a) -1
b) 1
c) 0
d) None of these
Answer: b
The elimination method is preferred over the substitution method when:
a) Coefficients of one variable are multiples of each other
b) Coefficients of one variable are equal
c) The equations are difficult to graph
d) Both a and b
Answer: d
The pair of equations
$2x + 3y = 5$
and
$4x + 6y = 15$
represents:
a) Parallel lines
b) Intersecting lines
c) Coincident lines
d) None of these
Answer: a
If the solution of
$3x + 4y = 10$
is $x = 2$ , then $y$ is:
a) 0
b) -1
c) 1
d) 2
Answer: c
If the equations
$5x – 3y = 2$
and
$10x – 6y = 4$
are solved, the lines will be:
a) Coincident
b) Intersecting
c) Parallel
d) None of these
Answer: a
A pair of linear equations is consistent if:
a) It has no solution
b) It has a unique solution
c) It has infinitely many solutions
d) Both b and c
Answer: d
The value of k for which the pair of equations
$kx + 3y = 7$
and
$2x + y = 4$
has a unique solution is:
a)
$k = 2$

b)
$k \neq 2$

c)
$k = -3$

d) None of these
Answer: b
If the equations
$2x + 5y = 7$
and
$4x + 10y = 14$
are solved, the solution will be:
a) Unique
b) Infinitely many
c) No solution
d) None of these
Answer: b
If
$x + 2y = 5$
and
$x – y = 2$
then the value of x is:
a) 3
b) 4
c) 2
d) None of these
Answer: a
If the solution of
$2x + y = 7$
is
$x = 2, y = 3$
then the constant term is:
a) 5
b) 7
c) 3
d) 2
Answer: b
The substitution method is not convenient when:
a) Coefficients of one variable are difficult to simplify
b) The equations are already solved for one variable
c) The solution is an integer
d) None of these
Answer: a
The point of intersection of
$x + y = 6$
and
$x – y = 4$
is:
a) (5, 1)
b) (4, 2)
c) (6, 0)
d) None of these
Answer: a
A consistent pair of linear equations can have:
a) No solution
b) Exactly one solution
c) Infinitely many solutions
d) Both b and c
Answer: d
The lines
$3x + 4y = 10$
and
$6x + 8y = 20$
are:
a) Intersecting
b) Coincident
c) Parallel
d) None of these
Answer: b
If the lines
$2x + 3y = 6$
and
$4x + 6y = 8$
are graphed, they will:
a) Be parallel
b) Coincide
c) Intersect
d) None of these
Answer: a
The pair of equations
$x + y = 2$
and
$2x + 2y = 4$
has:
a) No solution
b) A unique solution
c) Infinitely many solutions
d) None of these
Answer: c
A dependent pair of equations has:
a) No solution
b) A unique solution
c) Infinitely many solutions
d) None of these
Answer: c
The elimination method simplifies a pair of equations into:
a) A single equation in two variables
b) A single equation in one variable
c) A pair of simpler equations
d) None of these
Answer: b
The solution of
$x + 3y = 9$
and
$2x – y = 4$
is:
a)
$x = 5, y = 3$

b)
$x = 3, y = 2$

c)
$x = 4, y = 1$

d) None of these
Answer: b
If
$x = 1$
and
$y = 2$
satisfy
$5x + 4y = k$
then $k$ is:
a) 8
b) 10
c) 13
d) 9
Answer: c
If
$x + y = 10$
and
$x – y = 2$
the solution is:
a)
$x = 6, y = 4$

b)
$x = 7, y = 3$

c)
$x = 5, y = 5$

d) None of these
Answer: a
The solution of the equations
$2x + 4y = 12$
and
$3x + 6y = 18$
is:
a) No solution
b) Unique solution
c) Infinitely many solutions
d) None of these
Answer: c
The point of intersection of the equations
$x + y = 7$
and
$2x – y = 4$
is:
a) (4, 3)
b) (3, 4)
c) (5, 2)
d) None of these
Answer: c

Pair of Linear Equations in Two Variables

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