CBSE Class 10 Mental Maths Pair of Linear Equations in Two Variables Worksheet

Question. The pair of linear equations 3x/2 + 5y/3 = 7 and 9x + 10y = 14 is
(a) consistent
(b) inconsistent
(c) consistent with one solution
(d) consistent with many solutions
Answer : B

Question. Graphically, the pair of equations 6x - 3y + 10 = 0 and 2x - y + 9 = 0 represents two lines which are:
(a) intersecting at exactly one point.
(b) intersecting at exactly two points.
(c) coincident
(d) parallel
Answer : D

Question. 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
Answer : C

Question. The value of k for which the system of linear equation x + 2y = 3, 5x + ky + 7 = 0 is inconsistent is
(a) −14/3
(b) 2/5
(c) 5
(d) 10
Answer : D

Question. The value of k for which the system of equations x + y - 4 = 0 and 2x + ky = 3, has no solution, is
(a) -2
(b) ≠2
(c) 3
(d) 2
Answer : D

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

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

Question. For which value(s) of p, will the lines represented by the following pair of linear equations be parallel:
3x - y - 5 = 0
6x - 2y - p = 0
(a) all real values except 10
(b) 10
(c) 5/2
(d) 1/2
Answer : A

Question. If the lines given by 3x + 2ky = 2 and 2x + 5y + 1 = 0 are parallel, then the value of k is:
(a) - 5/4
(b) 2/5
(c) 15/4
(d) 3/2
Answer : C

Question. The pair of equations, x = 0 and x = - 4 has
(a) a unique solution
(b) no solution
(c) infinitely many solution
(d) only solution (0, 0)
Answer : B

Question. One equation of a pair of dependent linear equations 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

Question. 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
Answer : D

Question. If x = a, y = b is the solution of the equations x - y = 2 and x + y = 4, then the values of a and b respectively are:
(a) 3 and 5
(b) 5 and 3
(c) 3 and 1
(d) -1 and -3
Answer : C

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

Fill in the Blanks / True False

Fill in the blanks/tables with suitable information or answer whether True/False

Question. The value of k for which pair of linear equations 3x + 2y = -5 and x - ky = 2 has a unique solution is .................... .
Answer : k ≠ – 2/3

Question. The value of a so that the point (3, a), lies on the line represented by 2x - 3y = 5 is .................... .
Answer : 1/3

Question. The co-ordinate where the line x - y = 8 will intersect y-axis is .................... .
Answer : (0, – 8)

Question. The value of k for which the pair of linear equations kx + 3y = k - 2 and 12x + ky = k has no solution is .................... .
Answer : k = ± 6

Question. The graphical representation of the pair of equations x + 2y - 4 = 0 and 2x + 4y - 12 = 0 represents .................... .
Answer : Parallel lines

Question. If x + y = 2 and 1 / x + y = 2/5 then x = ................... .
Answer : 9/4

Question. The value of p for the following pair of linear equations (p - 3)x + 3y = p; px + py = 12 have infinitely many solutions is .................... .
Answer : p = 6

Question. If x = a, y = b is the solution of the pair of equation x - y = 2 and x + y = 4 then the value of 3a + 4b is .................... .
Answer : 13

Question. For all real values of c, the pair of equations
x - 2y = 8
5x - 10y = c
have a unique solution. Justify whether it is true or false. 
Answer : False