The pairs of linear equations which have the unique solution $x = 2, y = - 3$ are,

$x + y = - 1; 2 x + 3 y = - 5$

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

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$2 x - y = 1; 3 x + 2 y = 0$

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$x - 4 y - 14 = 0; 5 x - y - 13 = 0$

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Solution

The correct option is D
$x - 4 y - 14 = 0; 5 x - y - 13 = 0$

Option A:

$x + y = - 1 - - - - - (i)$

$2 x + 3 y = - 5 - - - - (i i)$

$(i) \times 2 \to 2 x + 2 y = - 2 - - - - (i i i)$

Solving by elimination $((i i i) - (i i))$ we get,

$x = 2 a n d y = - 3.$

Option D:

$x - 4 y = 14 - - - - (i)$

$5 x - y = 13 - - - - - (i i)$
$(i i) \times 4 \to 20 x - 4 y = 52 - - - - (i i i)$

Solving by elimination method $((i i i) - (i))$ we get,

$x = 2 a n d y = - 3$

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