Answer
$$x=-\frac{1}{2}$$ $$y=2$$
Work Step by Step
Equation 1: $\frac{1}{2}x+ 2y =\frac{15}{4}$
Equation 2: $4x = -y$
Multiply equation 2 by $-1$:
$$[4x = -y]\cdot-1$$ $$-4x = y$$
Substitute this equation to equation 1:
$$\frac{1}{2}x+ 2y =\frac{15}{4}$$ $$\frac{1}{2}x+ 2(-4x) =\frac{15}{4}$$ $$\frac{1}{2}x-8x =\frac{15}{4}$$ $$\frac{1}{2}x-\frac{16}{2}x =\frac{15}{4}$$ $$-\frac{15}{2}x =\frac{15}{4}$$
Divide both sides by $-\frac{15}{2}$:
$$\frac{-\frac{15}{2}x}{-\frac{15}{2}} =\frac{\frac{15}{4}}{-\frac{15}{2}}$$ $$x=\frac{15}{4}\cdot-\frac{2}{15}$$ $$x=-\frac{1}{2}$$
Substitute this value of $x$ to equation 2:
$$4x = -y$$ $$4(-\frac{1}{2})= -y$$ $$-2=-y$$ $$y=2$$
Use equation 1 to check:
$$\frac{1}{2}(-\frac{1}{2})+ 2(2) =\frac{15}{4}$$ $$-\frac{1}{4}+ 4 =\frac{15}{4}$$ $$-\frac{1}{4}+ \frac{16}{4} =\frac{15}{4}$$ $$\frac{15}{4}=\frac{15}{4}$$