Question

What is the solution to the system of equations 1/4x+1 1/2y=5/8 3/4x-1 1/2y=3 3/8

Answer 1

Answer:

$\large\boxed{x=4,\ y=-\dfrac{1}{4}}$

Step-by-step explanation:

$\underline{+\left\{\begin{array}{ccc}\dfrac{1}{4}x+1\dfrac{1}{2}y=\dfrac{5}{8}\\\\\dfrac{3}{4}x-1\dfrac{1}{2}y=3\dfrac{3}{8}\end{array}\right}\qquad\text{add both sides of the equations}\\.\qquad\dfrac{4}{4}x=3\dfrac{8}{8}\\\\.\qquad\boxed{x=4}\\\\\text{put the value of x to the first equation:}\\\\\dfrac{1}{4}(4)+1\dfrac{1}{2}y=\dfrac{5}{8}\\\\1+1\dfrac{1}{2}y=\dfrac{5}{8}\qquad\text{subtract}\ 1=\dfrac{8}{8}\ \text{from obth sides}\\\\1\dfrac{1}{2}y=-\dfrac{3}{8}\qquad\text{multiply both sides by 2}\\\\3y=-\dfrac{3}{4}\qquad\text{divide both sides by 3}\\\\\boxed{y=-\dfrac{1}{4}}$