# How do you solve the system 1/4x+y=3/4 and 3/2x-y=-5/2?

May 17, 2015

From the first equation we can derive a formula for $y$ by subtracting $\frac{1}{4} x$ from both sides to get

$y = \frac{3}{4} - \frac{1}{4} x$

Then substitute that for $y$ in the second equation:

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

$= \frac{3}{2} x - \left(\frac{3}{4} - \frac{1}{4} x\right)$

These fractions are a pain, so let's eliminate them by multiplying through by 4 to get:

$- 10 = 6 x - \left(3 - x\right) = 7 x - 3$

Now add 3 to both sides to get

$7 x = - 7$

Divide both sides by $7$ to get

$x = - 1$

Then $y = \frac{3}{4} - \frac{1}{4} x = \frac{3}{4} + \frac{1}{4} = 1$