Solve for x and y :4 x=17-x-y 8 ;2 y+x=2+5 y+2 3 - Vidyadip

Question

Solve for $\mathrm{x}$ and $\mathrm{y}$ :$4 x=17-\frac{x-y}{8};2 y+x=2+\frac{5 y+2}{3}$

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Answer

The given pair of linear equations are
$4 \mathrm{x}=17-\frac{x-y}{8}$
$\Rightarrow 33 x-y=136\dots ...(1)($ On Simplifying$)$
$2 y+x=2+\frac{5 y+2}{3}$
$\Rightarrow 3 x+y=8\dots...(2)($ On Simplifying $)$
Multiply equation $(2)$ by $11$ , we get,
$33 x+11 y=88\dots...(3)$
Subtracting equation $(1)$ from $(3)$
$\begin{gathered}33 x+11 y=88,-33 x-y=136,-+-,12 y=-48y=-4\end{gathered}$
Substituting $y=-4$ in equation $(1)$, we get :
$33 x-(-4)=136$
$ \Rightarrow 33 x=132$
$ \Rightarrow x=4$
$\therefore$ Solution is $\mathrm{x}=4$ and $\mathrm{y}=-4$.

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