Question

solve 5x-y=13, x-2y=7 by substitution method ​

Answer 1

$Given \: pair \: of \: equations :$

$5x - y = 13 \: ---(1) \\and \: x - 2y = 7 \implies x = 7 + 2y \: ---(2)$

/* Substitute x = 7 + 2y in equation (1), we get */

$5(7+2y) - y = 13$

$\implies 35 + 10y - y = 13$

$\implies 9y = 13 - 35$

$\implies 9y = -22$

$\implies y = \frac{-22}{9} \: ---(3)$

$Now, put \: y = \frac{-22}{9}\: in \: equation \\(2) , we \: get$

$x = 7 + 2 \times \Big(\frac{-22}{9}\Big) \\= 7 - \frac{44}{9} \\= \frac{63 - 44}{9} \\= \frac{19}{9}$

Therefore.,

$\green { x = \frac{19}{9}\: and \: y = \frac{-22}{9}}$

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