Question

Solve for $x$ and $y$:

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

• A. $x=4;y=-4$
• B. $x=1;y=-6$
• C. $x=-6;y=-3$
• D. $x=2;y=-7$

Answer 1

The correct option is A $x=4;y=-4$

Given equations are,

$4x=17-\frac{x-y}{8}$

$\Rightarrow 32x=136-x+y$

$\Rightarrow 33x-y=136$ ....(1)

and $2y+x=2+\frac{5y+2}{3}$

$\Rightarrow 3(2y+x)=6+5y+2$

$\Rightarrow 6y+3x=6+5y+2$

$\Rightarrow 3x+y=8$ ....(2)

Add equations (1) and (2), we get

$36x=144$

$\Rightarrow x=4$

Put this value in equation (1), we get

$33\left(4\right)-y=136$

$\Rightarrow 132-y=136$

$\Rightarrow y=-4$

Therefore, the solution is $x=4,y=-4$.