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## Pair of Linear Equations in Two Variables Class 10 MCQs Questions with Answers

Question 1.
Graphically, the pair of equations 6x – 3y + 10 = 0
2x – y + 9 = 0
represents two lines which are
(a) Intersecting at exactly one point
(b) Intersecting at two points
(c) Coincident
(d) Parallel

Question 2.
The pair of linear equations x + 2y + 5 = 0 and -3x – 6y + 1 = 0 has
(а) a unique solution
(b) exactly two solutions
(c) infinitely many solutions
(d) no solutions

Question 3.
If a pair of linear equations is consistent, then
the lines will be
(a) parallel
(b) always coincident
(c) intersecting or coincident
(d) always intersecting

Question 4.
The pair of equations y = 0 and y = -7 has
(а) one solution
(b) two solutions
(c) infinitely many solutions
(d) no solution

Question 5.
The pair of equations x = a and y = b graphically represents lines which are
(а) parallel
(b) intersecting at (b, a)
(c) coincident
(d) intersecting at (a, b)

Answer: (d) intersecting at (a, b)

Question 6.
For what value of k, for the equations 3x – y + 8 = 0 and 6x – ky = -16 represents coincident lines?
(a) $$\frac{1}{2}$$
(b) –$$\frac{1}{2}$$
(c) 2
(d) -2

Question 7.
If the lines given by 3x + 2ky = 2 and 2x + 5y + 1 = 0 are parallel, then the value of k is
(a) –$$\frac{5}{4}$$
(b) –$$\frac{2}{5}$$
(c) $$\frac{15}{4}$$
(d) –$$\frac{3}{2}$$

Answer: (c) $$\frac{15}{4}$$

Question 8.
The value of c for which the pair of equations cx – y = 2 and 6x – 2y = 3 will have infinitely many solutions is
(a) 3
(b) -3
(c) -12
(d) no value

Question 9.
One equation of a pair of dependent linear equation is -5x + 7y = 2. The second equation can be
(a) 10x + 14y + 4 = 0
(b) -10x – 14y + 4 = 0
(c) -10x + 14y + 4 = 0
(d) 10x – 14y = -4

Answer: (d) 10x – 14y = -4

Question 10.
A pair of linear equations which has a unique solution x = 2, y = -3 is
(a) x + y = -1
2x – 3y = -5
(b) 2x + 5y = -11
4x + 10y = -22
(c) 2x – y = 1
3x + 2y = 0
(d) x – 4y – 14 = 0
5x – y – 13 = 0

Answer: (d) x – 4y – 14 = 0
5x – y – 13 = 0

Question 11.
If x = a, y = b is the solution of the equation x – y = 2 and x + y = 4, then the value of a and b are respectively
(a) 3 and 5
(b) 5 and 3
(c) 3 and 1
(d) -1 and -3

Question 12.
Aruna has only Rs 1 and Rs 2 coins with her. If the total number of coins that she has is 50 and the amount of money with her is Rs 75, then the number of Rs 1 and Rs 2 coins are respectively
(a) 35 and 15
(b) 35 and 20
(c) 15 and 35
(d) 25 and 25

Question 13.
The father’s age is six times his son’s age. Four years hence, the age of the father will be four times his son’s age. The present ages of the son and the father, in years, are respectively
(a) 4 and 24
(b) 5 and 30
(c) 6 and 36
(d) 3 and 24

Question 14.
If the system of equations 2x + 3y = 7
2ax + (a + 6)y = 28
has infinitely many solutions, then
(a) a = 2b
(b) b = 2a
(c) a + 2b = 0
(d) 2a + b = 0

Question 15.
The angles of a triangle are x, y and 40°. The difference between the two angles x and y is 30°. The values of x and y are
(a) 45°, 75°
(b) 50°, 80°
(c) 55°, 85°
(d) 55°, 95°