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A pair of linear equations which has a unique solution $x = 2$ and $y = − 3$ is:

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6 x + 7 y = − 11, 6 x + 7 y = − 22

5 x + 5 y = − 11, 7 x + 7 y = − 22

3 x + 5 y = − 11, 7 x + 10 y = − 22

2 x + 5 y = − 11, 4 x + 10 y = − 22

answer is D.

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Detailed Solution

A unique solution satisfies the pair of linear equations.
Since

x = 2, y = − 3

is a unique solution for a pair of the equations, then these values must satisfy that pair of equations.
For option (1),

6 x + 7 y = − 11 L H S, = 6 (2) + 7 (− 3) = 12 − 21 = − 9 L H S ≠ R H S 6 x + 7 y = − 22 L H S, = 6 (2) + 7 (− 3) = 12 − 21 = − 9 L H S ≠ R H S

For option (2),

5 x + 5 y = − 11 L H S, = 5 (2) + 5 (− 3) = 10 − 15 = − 5 L H S ≠ R H S 7 x + 7 y = − 22 L H S, = 7 (2) + 7 (− 3) = 14 − 21 = − 7 L H S ≠ R H S

For option (3),

3 x + 5 y = − 11 L H S, = 3 (2) + 5 (− 3) = 6 − 15 = − 9 L H S ≠ R H S 7 x + 10 y = − 22 L H S, = 7 (2) + 10 (− 3) = 14 − 30 = − 16 L H S ≠ R H S

For option (4),

2 x + 5 y = − 11 L H S, = 2 (2) + 5 (− 3) = 4 − 15 = − 11 L H S = R H S 4 x + 10 y = − 22 L H S, = 4 (2) + 10 (− 3) = 8 − 30 = − 22 L H S = R H S

Therefore, a pair of linear equations which has a unique solution

x = 2

and

y = − 3

2 x + 5 y = − 11, 4 x + 10 y = − 22

.
Hence, option (4) is correct.

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