Solution of a Linear

-16x=2y-10

• 8x+y=5

• -16x-2y=10

• 16x+2y=-10

• 8x-y=-5

If x=a and y=b is the solution of the equations 2x+ y = 3 and x-y =3, then find the values of a and b

( 1 mark )

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The linear equation 3x - 5y = 15 has

• a unique solution

• two solutions

• infinitely many solutions

• no solution

• 5

• 6

• 7

• 8

Check which of the following options is not the solution of the equation: 2x – y = 6

• (2, 4)

• (3, 0)

• (7/2,1)

• (2, -2)

Answer explanation

2x - y = 6 Taking (x = 2, y = 4) L.H.S = 2(2) - 4 = 0 ≠ R.H.S Therefore, (2, 4) is not the correct solution of the equation 2x - y = 6 Options 2, 3 and 4 are the solutions of the equation 2x - y = 6

Find the value of k, if x = - 2, y = 3 is a solution of the equation: 5x + 6y = k

• k = 6

• k = - 8

• k = - 4

• k = 8

Answer explanation

5x + 6y = k Taking (x = -2, y = 3), we get, 5(- 2) + 6(3) = k - 10 + 18 = k k = 8 Therefore, value of k = 8

The linear equation x = 3y + 5 has _____

• No Solution

• Only two solutions

• A unique Solution

• Infinitely many Solutions

Answer explanation

Put y = 0, x = 3(0) + 5, we will get x = 5..... (5, 0) Put y = 1, x = 3(1) + 5, we will get x = 8..... (8, 1) Put y = 10, x = 3(10) + 5, we will get x = 35..... (35, 10) A linear equation in two variables has infinitely many solutions. So,x = 3y + 5 has infinitely many solutions.

Identify the option having two correct solutions for the equation 5x + 4y = 20

• (2,1) and (3,2)

• (1, 4) and (3,1)

• (0, 5) and (4, 0)

• (4, 3) and (3, 0)

Answer explanation

5x + 4y = 20 On taking (x = 0, y = 5), L.H.S = 5(0) + 4(5) = 20 = R.H.S On taking (x = 4, y = 0), L.H.S = 5(4) + 4(0) = 20 = R.H.S Therefore, (0, 5) and (4, 0) are two solutions of the given linear equation in two variables.

Check which of the following options is not the solution of the equation: 7x – 4y = 16

• (0, - 4)

• (16/7, 0)

• (5, 2)

• (2, -1/2)

Answer explanation

7x – 4y = 16 Taking (x = 5, y = 2) L.H.S = 7(5) - 4(2) = 27 ≠ R.H.S Therefore,(5, 2) is not the solution of the equation 7x – 4y = 16 whereas the remaining options are the solutions of this equation. Therefore option 3 is the correct answer.

x = 4, y = 6 is a solution of the linear equation

• x + 6 y = 10

• 4x + 6y = 10

• x + y = 10

• 4 x + y = 10

Answer explanation

Substituting x=4 and y=6 in option 1, LHS= 4 + 6(6) = 4 + 36 = 40 ≠ RHS Therefore, option 1 is incorrect Substituting x=4 and y=6 in option 2, LHS= 4(4) + 6(6) = 16 + 36 = 52 ≠ RHS Therefore, option 2 is incorrect Substituting x=4 and y=6 in option 3, LHS= 4 + 6 = 10 = RHS Therefore, option 3 is the correct answer. Substituting x=4 and y=6 in option 4, LHS= 4(4) + 6 = 16 + 6 = 22 ≠ RHS Therefore, option 4 is incorrect