# How do you solve the following system?:  1/4x-3/7y=1 , 3/2x - 8y = 2

May 14, 2016

$x = \frac{24}{19}$ and $y = \frac{14}{19}$

#### Explanation:

Given the system:

$\frac{1}{4} x - \frac{3}{7} y = 1$

$\frac{3}{2} x - 8 y = 2$

Multiply the first equation by $4$ to get:

$x - \frac{12}{7} y = 4$

Add $\frac{12}{7} y$ to both sides to get:

$x = \frac{12}{7} y + 4$

Substitute this expression for $x$ in the second equation to get:

$2 = \frac{3}{2} \left(\frac{12}{7} y + 4\right) - 8 y$

$= \frac{18}{7} y + 6 - 8 y$

$= \frac{18 - 56}{7} y + 6$

$= - \frac{38}{7} y + 6$

Add $\frac{38}{7} y - 2$ to both ends to get:

$\frac{38}{7} y = 4$

Multiply both sides by $\frac{7}{38}$ to get:

$y = \frac{14}{19}$

Then we find:

$x = \frac{12}{7} y + 4 = \frac{12}{7} \left(\frac{14}{19}\right) + 4 = \frac{24}{19}$