Answer
Solution: $(-2,\frac{3}{4})$
Work Step by Step
$\frac{1}{8}x-\frac{1}{2}y=\frac{-5}{8}$ Equation $(1)$
$-3x-8y=0$ Equation $(2)$
Multiply Equation $(1)$ by LCD $8$ to eliminate fractions.
$8(\frac{1}{8}x-\frac{1}{2}y)=8(\frac{-5}{8})$
$8(\frac{1}{8}x)-8(\frac{1}{2}y)=8(\frac{-5}{8})$
$x-4y=-5$ Equation $(3)$
Multiply Equation $(3)$ by 3 and add with Equation $(2)$ to eliminate $x$.
$3(x-4y) -3x-8y =-5 \times 3 + 0$
$3x-12y -3x -8y = -15$
$-20y = -15$
$y = \frac{-15}{-20} = \frac{3}{4}$
Substituting $y$ value in Equation $(2)$
$-3x-8y=0$
$-3x-8(\frac{3}{4})=0$
$-3x-6=0$
$-3x=6$
$x=-2$
Solution: $(-2,\frac{3}{4})$
