Question

Solve for $x$ and $y$:
$\frac{7+x}{5}-\frac{2x-y}{4}=3y-5$ and $\frac{5y-7}{2}+\frac{4x-3}{6}=18-5x$

Answer 1

$\frac{7+x}{5}-\frac{2x-y}{4}=3y-5$

$\frac{5y-7}{2}+\frac{4x-3}{6}=18-5x$

simplifying the first, we get

$4(7+x)-5(2x-y)=20(3y-5)$

$28+4x-10x+5y-60y=-100$

$-6x-55y=-128$

$6x+55y=128...\left(1\right)$

simplifying the second equation, we get

$6(5y-7)+2(4x-3)=12(18-5x)$

$30y-42+8x-6=216-60x$

$68x+30y=216+48$

$34x+15y=\frac{264}{2}=132...\left(2\right)$

$\left(1\right)\times 3\Rightarrow 18x+165y=384$

$\left(2\right)\times 11\Rightarrow 374x+165y=1452$

$\left(2\right)\times 11-\left(1\right)\times 3=356x=1068$

$x=\frac{1068}{356}=3$

sub $x=3$ in $\left(1\right)\Rightarrow 55y=128-18=110$

$y=\frac{110}{55}=2$

$\therefore x=3;y=2.$