Solve the following pair of equations using cross multiplication method.
x + 2y = -2 , x - y = 4

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Solution

Given equations are,

$x + 2 y = - 2, \Rightarrow x + 2 y + 2 = 0 \dots \dots (i)$

Comparing this equation with $a_{1} x + b_{1} y + c_{1} = 0$ , we get
$a_{1} = 1, b_{1} = 2, c_{1} = 2$

$x - y = 4, \Rightarrow x - y - 4 = 0 \dots \dots (i i)$

Comparing this equation with $a_{2} x + b_{2} y + c_{2} = 0$ , we get
$a_{2} = 1, b_{2} = - 1, c_{2} = - 4$

From cross multiplication method, we have,
$x = \frac{b_{1} c_{2} - b_{2} c_{1}}{a_{1} b_{2} - a_{2} b_{1}}$ , $y = \frac{c_{1} a_{2} - c_{2} a_{1}}{a_{1} b_{2} - a_{2} b_{1}}$

$x = \frac{[(2) (- 4) - (- 1) (2)]}{(1) (- 1) - (1) (2)}$

$x = \frac{[(- 8) - (2)]}{(- 1) - (2)}$

$\Rightarrow x = 2$

$y = \frac{c_{1} a_{2} - c_{2} a_{1}}{a_{1} b_{2} - a_{2} b_{1}}$

$y = \frac{[(2) (1) - (- 4) (1)]}{(1) (- 1) - (1) (2)}$

$y = \frac{[(2) - (- 4)]}{(- 1) - (2)}$

$\Rightarrow y = - 2$

$∴$ $x = 2$ , $y = - 2$

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