# How do you solve the following system?: -21x+3y=21 , -6x+3y=17

Nov 29, 2015

$\left(- \frac{4}{15} , \frac{77}{15}\right)$

#### Explanation:

Given system of equation
$- 21 x + 3 y = 21 \text{ " " " " } \left(1\right)$
$- 6 x + 3 y = 17 \text{ " " " " } \left(2\right)$

Multiply the first equation by $- 1$

$- 1 \cdot \left(- 21 x + 3 y = 21\right)$

$21 x - 3 y = - 21 \text{ " } \left(3\right)$

Add equation $\left(2\right)$ from equation $\left(3\right)$

$21 x - 3 y = - 21$
$- 6 x + 3 y = 17$
stackrel("--------------------------------")

$15 x = - 4$

$\textcolor{red}{x = - \frac{4}{15}}$

Substitute $x = - \frac{4}{15}$ for $y$ in equation $\left(1\right)$

$- 21 \cdot \left(- \frac{4}{15}\right) + 3 y = 21$

$\frac{28}{5} + 3 y = 21$

$5 \left(\frac{28}{5} + 3 y = 21\right)$

$28 + 15 y = 105$

$15 y = 77$

$\textcolor{red}{y = \frac{77}{15}}$