Solve :4 x+x-y 8 =17,2 y+x-5 y+2 3 =2 - Vidyadip

Question

Solve :$4 x+\frac{x-y}{8}=17,2 y+x-\frac{5 y+2}{3}=2$

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Answer

$4 x+\frac{x-y}{8}=17 ($Given$)$
$\Rightarrow 32 x+x-y=136$
$\Rightarrow 33 x-y=136 \dots......(1)$
$2 y+x-\frac{5 y+2}{3}=2 ($Given$)$
$\Rightarrow 6 y+3 x-5 y-2=6$
$\Rightarrow 3 x+y=8\dots.......(2)$
Adding equations $(1)$ and $(2),$ we get
$33 x-y =136$
$+ 3 x+y =8$
$36 x =144$
$x =4$
Substituting $x=4$ in equation $(2),$ We get
$3 \times 4+y=8$
$ \Rightarrow 12+y=8$
$ \Rightarrow y=8-12$
$ \Rightarrow y=-4$
$ \therefore$ Solution is $x=4$ and $y=-4$

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