Pair of Linear Equations in Two Variables

A pair of linear equations in two variables can be represented as:
a)
ax2+by+c=0ax^2 + by + c = 0
b)
ax+by+c=0ax + by + c = 0
c)
ax3+by2+c=0ax^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)
a1a2≠b1b2\frac{a_1}{a_2} \neq \frac{b_1}{b_2}
b)
a1a2=b1b2≠c1c2\frac{a_1}{a_2} = \frac{b_1}{b_2} \neq \frac{c_1}{c_2}
c)
a1a2=b1b2=c1c2\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=2x – y = 2
and
3x−3y=63x – 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=62x + 3y = 6
and
4x+6y=124x + 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)
a1x2+b1y+c1=0a_1x^2 + b_1y + c_1 = 0
b)
a1x+b1y+c1=0a_1x + b_1y + c_1 = 0
and
a2x+b2y+c2=0a_2x + b_2y + c_2 = 0
c)
a1x+b1y+c1=0a_1x + b_1y + c_1 = 0
and
a2x2+b2y+c2=0a_2x^2 + b_2y + c_2 = 0
d) None of these
Answer: b
If
5x−3y=25x – 3y = 2
and
3x−2y=13x – 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)
a1a2≠b1b2\frac{a_1}{a_2} \neq \frac{b_1}{b_2}
b)
a1a2=b1b2≠c1c2\frac{a_1}{a_2} = \frac{b_1}{b_2} \neq \frac{c_1}{c_2}
c)
a1a2=b1b2=c1c2\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=5x + y = 5
and
x−y=1x – y = 1
is:
a)
x=3,y=2x = 3, y = 2
b)
x=2,y=3x = 2, y = 3
c)
x=−1,y=−2x = -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=52x + 3y = 5
and
4x+6y=104x + 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=6x + 2y = 6
and
2x+4y=122x + 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=7x + y = 7
and
x−y=3x – y = 3
is:
a)
x=5,y=2x = 5, y = 2

b)
x=4,y=3x = 4, y = 3

c)
x=6,y=1x = 6, y = 1

d) None of these
Answer: a
The condition for a pair of linear equations to have no solution is:
a)
a1a2≠b1b2\frac{a_1}{a_2} \neq \frac{b_1}{b_2}

b)
a1a2=b1b2≠c1c2\frac{a_1}{a_2} = \frac{b_1}{b_2} \neq \frac{c_1}{c_2}

c)
a1a2=b1b2=c1c2\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=73x + 4y = 7
and
6x+8y=146x + 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=3x = 2, y = 3
is a solution of the equation
ax+by=12ax + by = 12
then
a+ba + b
is:
a) 5
b) 6
c) 7
d) 4
Answer: a
The pair of equations
x+y=10x + y = 10
and
2x+2y=202x + 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=4x + y = 4
and
x−y=2x – y = 2
will show:
a) Parallel lines
b) Intersecting lines
c) Coincident lines
d) None of these
Answer: b
If
x=0x = 0
and
y=−1y = -1
satisfies
ax+by=−1ax + 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=52x + 3y = 5
and
4x+6y=154x + 6y = 15
represents:
a) Parallel lines
b) Intersecting lines
c) Coincident lines
d) None of these
Answer: a
If the solution of
3x+4y=103x + 4y = 10
is $x = 2$ , then $y$ is:
a) 0
b) -1
c) 1
d) 2
Answer: c
If the equations
5x−3y=25x – 3y = 2
and
10x−6y=410x – 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=7kx + 3y = 7
and
2x+y=42x + y = 4
has a unique solution is:
a)
k=2k = 2

b)
k≠2k \neq 2

c)
k=−3k = -3

d) None of these
Answer: b
If the equations
2x+5y=72x + 5y = 7
and
4x+10y=144x + 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=5x + 2y = 5
and
x−y=2x – 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=72x + y = 7
is
x=2,y=3x = 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=6x + y = 6
and
x−y=4x – 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=103x + 4y = 10
and
6x+8y=206x + 8y = 20
are:
a) Intersecting
b) Coincident
c) Parallel
d) None of these
Answer: b
If the lines
2x+3y=62x + 3y = 6
and
4x+6y=84x + 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=2x + y = 2
and
2x+2y=42x + 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=9x + 3y = 9
and
2x−y=42x – y = 4
is:
a)
x=5,y=3x = 5, y = 3

b)
x=3,y=2x = 3, y = 2

c)
x=4,y=1x = 4, y = 1

d) None of these
Answer: b
If
x=1x = 1
and
y=2y = 2
satisfy
5x+4y=k5x + 4y = k
then $k$ is:
a) 8
b) 10
c) 13
d) 9
Answer: c
If
x+y=10x + y = 10
and
x−y=2x – y = 2
the solution is:
a)
x=6,y=4x = 6, y = 4

b)
x=7,y=3x = 7, y = 3

c)
x=5,y=5x = 5, y = 5

d) None of these
Answer: a
The solution of the equations
2x+4y=122x + 4y = 12
and
3x+6y=183x + 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=7x + y = 7
and
2x−y=42x – y = 4
is:
a) (4, 3)
b) (3, 4)
c) (5, 2)
d) None of these
Answer: c