Solve for $^{'} x^{'}$ and $^{'} y^{'}$ $2 x - 3 y = 13, 7 x - 2 y = 20$

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Solution

$2 x - 3 y = 13 ⟶ (i) 7 x - 2 y = 20 ⟶ (i i)$
Multiplying $(i)$ by $2$ and $(i i)$ by $3$
$4 x - 6 y = 26 21 x - 6 y = 60$
On subtraction : $- 17 x = - 34$
$x = 2$
putting the value of $x$ in $(i)$
$2 (2) - 3 y = 13 \Rightarrow - 3 y = 9 ∴ y = - 3$

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