Direct Answer:

Option C

Given:

★ The value of x and y as 4 and 2 respectively.

★ Four PAIRS of linear EQUATIONS namely:

a. x + y = 6,   x - y = 1

b. x + y = 6,  2x + 3y = 9

c. x - y = 2,  2x + y = 10

d. x + y = 6,  x - y = -2

To Find:

Which pair of the given linear equations will have x = 4 and y = 2 as their solutions.

Solution:

In order to find the pair of linear equations with x = 4 and y = 2 as their solutions, we need to substitute the value of x and y with the given values and check whether the answer we get on solving is equal to the RHS.

Option a

No.1  x + y = 6

x = 4 , y = 2

Substituting the values into the LHS,

4 + 2 = 6

LHS = RHS.

No.2  x - y = 1

Substituting the values into the LHS,

4 - 2 = 2

2 ≠ 1

LHS ≠ RHS

The given values are not the solutions of the given pair of equations.

Option b

No.1 x + y = 6

Substituting the values into the LHS,

4 + 2 = 6

LHS = RHS.

No.2 2x + 3y = 9

Substituting the values into the LHS,

(2 x 4) + (3 x 2)

= 8 + 6 = 14

14 ≠ 9

LHS ≠ RHS

The given values are not the solutions of the given pair of equations.

Option c

No.1 x - y = 2

Substituting the values into the LHS,

4 - 2 = 2

LHS = RHS

No.2 2x + y = 10

Substituting the values into the LHS,

(2 x 4) + 2

= 8 + 2 = 10

LHS = RHS

The given values are the solutions of the given pair of equations.

Option d

No.1 x + y = 6

Substituting the values into the LHS,

4 + 2 = 6

LHS = RHS

No.2 x - y = -2

Substituting the values into the LHS,

4 - 2 = 2

LHS ≠ RHS

The given values are not the solutions of the given pair of equations.

From the above observations, we can CONCLUDE that Option C is the pair of linear equations that has the given values of x and y as the solution.

a. x + y = 6,   x - y = 1

b. x + y = 6,  2x + 3y = 9

c. x - y = 2,  2x + y = 10 ✔

d. x + y = 6,  x - y = -2