CH3. PAIR OF LINEAR EQUATIONS IN TWO VARIABLES
1. The value of c, for which the pair of equations cx – y =2 and 6x – 2y =3 have infinitely many
solutions is
a) 3 b) -3 c) -12 d) no value
2. If a pair of equations is consistent, then the lines will be
a) parallel b) coincident c) intersecting d) intersecting or coincident
3. The value of k, for which the system of equations kx – y =2 and 6x – 2y =3 has unique
solution is
a) k = 3 b) k ≠ 3 c) k = 0 d) k ≠0
4. The difference between two numbers is 14 and the difference between their squares is 448,
then the numbers are
a) 22 and 9 b) 23 and 9 c) 25 and 9 d) none of these
5. If bx + ay = a2 + b2 and ax – by = 0, then the value of x – y is
a) a – b b) b – a c) a2 + b2 d) a2 – b2
6. The coordinates of vertices of triangle formed between the lines and
y axis from the graph is
a) (0,0), (0,5) and (6.5,0) b) (4,2), (0,0) and (6.5,0)
c) (4,2), (0,0) and (0,5) d) none of these
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7. The pair of equations 5x — 15y = 8 and 3x — 9y = 5
a) one solution b) two solutions c) infinitely many solutions d) no solution
8. If the lines 3𝑥 + 2𝑘𝑦 = 2 and 2𝑥 + 5𝑦 + 1 = 0 are parallel, find the value of k.
−5 3 15 2
a) b) c) d)
4 2 4 5
9. One equation of a pair of dependent linear equations is -5x+7y = 2. The second equation
will be:
a) 10𝑥 + 14𝑦 + 4 = 0 b) −10𝑥 – 14𝑦 + 4 = 0
c) −10𝑥 + 14𝑦 + 4 = 0 d) 10𝑥 – 14𝑦 = – 4
10. A pair of linear equations which has a unique solution x = 2 , y = -3 is
a) 𝑥 + 𝑦 = −1 and 2𝑥 – 3𝑦 = −5 b) 2𝑥 + 5𝑦 = −11 and 4𝑥 + 10𝑦 = −22
c) 2𝑥 – 𝑦 = 1 and 3𝑥 + 2𝑦 = 0 d) 𝑥 – 4𝑦 – 14 = 0 and 5x – y – 13 = 0
1. The value of c, for which the pair of equations cx – y =2 and 6x – 2y =3 have infinitely many
solutions is
a) 3 b) -3 c) -12 d) no value
2. If a pair of equations is consistent, then the lines will be
a) parallel b) coincident c) intersecting d) intersecting or coincident
3. The value of k, for which the system of equations kx – y =2 and 6x – 2y =3 has unique
solution is
a) k = 3 b) k ≠ 3 c) k = 0 d) k ≠0
4. The difference between two numbers is 14 and the difference between their squares is 448,
then the numbers are
a) 22 and 9 b) 23 and 9 c) 25 and 9 d) none of these
5. If bx + ay = a2 + b2 and ax – by = 0, then the value of x – y is
a) a – b b) b – a c) a2 + b2 d) a2 – b2
6. The coordinates of vertices of triangle formed between the lines and
y axis from the graph is
a) (0,0), (0,5) and (6.5,0) b) (4,2), (0,0) and (6.5,0)
c) (4,2), (0,0) and (0,5) d) none of these
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7. The pair of equations 5x — 15y = 8 and 3x — 9y = 5
a) one solution b) two solutions c) infinitely many solutions d) no solution
8. If the lines 3𝑥 + 2𝑘𝑦 = 2 and 2𝑥 + 5𝑦 + 1 = 0 are parallel, find the value of k.
−5 3 15 2
a) b) c) d)
4 2 4 5
9. One equation of a pair of dependent linear equations is -5x+7y = 2. The second equation
will be:
a) 10𝑥 + 14𝑦 + 4 = 0 b) −10𝑥 – 14𝑦 + 4 = 0
c) −10𝑥 + 14𝑦 + 4 = 0 d) 10𝑥 – 14𝑦 = – 4
10. A pair of linear equations which has a unique solution x = 2 , y = -3 is
a) 𝑥 + 𝑦 = −1 and 2𝑥 – 3𝑦 = −5 b) 2𝑥 + 5𝑦 = −11 and 4𝑥 + 10𝑦 = −22
c) 2𝑥 – 𝑦 = 1 and 3𝑥 + 2𝑦 = 0 d) 𝑥 – 4𝑦 – 14 = 0 and 5x – y – 13 = 0
