Question
Solve the pair of linear $($simultaneous$)$ equation by the method of elimination by substitution :$8x + 5y = 9,3x + 2y = 4$
✓
Answer
$ 8 x+5 y=9$
$3 x+2 y=4 \ldots(1)$
$8 x+5 y=9$
$\therefore 5 y=9-8 x$
$\therefore y=\frac{9-8 x}{5} \ldots .(2) $
Putting this value of $y$ in $(2)$
$ 3 x+2\left[\frac{9-8 x}{5}\right]=4 $
Multiplying by $5 ,$
$ 15 x+18-16 x=20$
$15 x-16 x=20-18$
$-x=2$
$x=-2 $
From $(3)$
$\ y=\frac{9-8 x}{5}$
$=\frac{9-8(-2)}{5}$
$=\frac{25}{5}$
$=5$
$ y=5 $
$3 x+2 y=4 \ldots(1)$
$8 x+5 y=9$
$\therefore 5 y=9-8 x$
$\therefore y=\frac{9-8 x}{5} \ldots .(2) $
Putting this value of $y$ in $(2)$
$ 3 x+2\left[\frac{9-8 x}{5}\right]=4 $
Multiplying by $5 ,$
$ 15 x+18-16 x=20$
$15 x-16 x=20-18$
$-x=2$
$x=-2 $
From $(3)$
$\ y=\frac{9-8 x}{5}$
$=\frac{9-8(-2)}{5}$
$=\frac{25}{5}$
$=5$
$ y=5 $
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