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

Solution:

Given, the solution to a pair of linear equations is x = 2 and y = -3.

We have to find the pair of linear equations.

If x = 2 and y = - 3 is a unique solution of any pair of equations, then these values must satisfy that pair of equations.

Substituting the values in each equation,

From the given options,

A) x + y = -1: 2x - 3y = -5

LHS: x + y = 2 - 3 = -1

RHS = -1

LHS = RHS

LHS: 2x - 3y = 2(2) - 3(-3) = 4 + 9 = 13

RHS = -5

LHS ≠ RHS

Therefore, option A is false.

B) 2x + 5y = -11; 4x + 10y = -22

LHS: 2x + 5y = 2(2) + 5(-3)

= 4 - 15

= -11

RHS = -11

LHS = RHS

LHS: 4x + 10y = 4(2) + 10(-3)

= 8 - 30

= -22

RHS = -22

LHS = RHS

Therefore, option B is true.

C) 2x - y = 1; 3x + 2y = 0

LHS: 2x - y = 2(2) - 3

= 4 - 1

= 3

RHS = 1

LHS ≠ RHS

LHS: 3x + 2y = 3(2) + 2(-3)

= 6 - 6

= 0

RHS = 0

LHS = RHS

Therefore, option C is false.

D) x - 4y -14 = 0; 5x - y - 13 = 0

x - 4y = 14

LHS: x - 4y

= 2 - 4(-3)

= 2 + 12

= 14

RHS = 14

LHS = RHS

5x - y = 13

LHS: 5x - y

= 5(2) - (-3)

= 10 + 3

= 13

RHS = 13

LHS = RHS.

Therefore, option D is true.

Therefore, a pair of linear equations which has a unique solution x = 2, y = -3 are 2x + 5y = -11; 4 x + 10y = -22 and x - 4y -14 = 0; 5x - y - 13 = 0.

✦ Try This: A pair of linear equations which has a unique solution x = 2, y = 3 is, a. x + y = 5; 2x - 3y = -5, b. 2x + 5y = -11; 4 x + 10y = -22, c. 2x - y = 1; 3x + 2y = 0, d. x - 4y - 14 = 0; 5x - y - 13 = 01

☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 3

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NCERT Exemplar Class 10 Maths Exercise 3.1 Problem 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

Summary:

A pair of linear equations which has a unique solution x = 2, y = -3 are 2x + 5y = -11; 4 x + 10y = -22 and x - 4y -14 = 0; 5x - y - 13 = 0

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