Choose the correct answer from the given four options : A pair of… - Vidyadip

MCQ

Choose the correct answer from the given four options : A pair of linear equations which has a unique solution $x = 2, y = -3$ is :

A
$x + y = -1, 2x - 3y = -5.$
✓
$2x + 5y = -11, 4x + 10y = -22.$
C
$2x - y = 1, 3x + 2y = 0.$
D
$x - 4y -14 = 0, 5x - y - 13 = 0.$

✓

Answer

Correct option: B.

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

If $x = 2, y = -3$ is a unique solution of any pair of equation,
then these values must satisfy that pair of equations.
From option $(b), \text{LHS} = 2x + 5y = 2(2) + 5(-3) = 4 -15 = -11 = \text{RHS}$
and $\text{LHS} = 4x + 10y = 4(2) + 10(-3) = 8 - 30 = -22 = \text{RHS}.$

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