Solve
$3 x + 2 y = 8$
$2 x - 3 y = 1$

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Solution

$3 x + 2 y = 8 - (1)$
$2 x - 3 y = 1 - (2)$

Multiply equation $(1)$ by $3$ and $(2)$ by $2$ we get,
$9 x + 6 y = 24 - (3)$
$4 x - 6 y = 2 - (4)$

Adding equations $(2)$ and $(4)$ we get
$(9 x + 6 y) + (4 x - 6 y) = 24 + 2$
$\Rightarrow 13 x = 26$
$\Rightarrow x = 2$

Substitute $x = 2$ in equation $(1),$
$3 x + 2 y = 8$
$\Rightarrow 3 \times 2 + 2 y = 8$
$\Rightarrow 6 + 2 y = 8$
$\Rightarrow 2 y = 2$
$\Rightarrow y = 1$

Hence, the solution for the given system of equation is $(2, 1) .$

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