# How do solve the following linear system?:  -8x + y = 2 , 8x + 3y= -9 ?

Feb 7, 2016

Solve by elimination and substitution:

$- 8 x + y = 2 , 8 x + 3 y = - 9$

Eliminate $8 x$ from the second equation by $- 8 x$ in the first equation:

$\rightarrow \left(- 8 x + y = 2\right) + \left(8 x + 3 y = - 9\right)$

$\rightarrow 4 y = - 7$

$\rightarrow y = - \frac{7}{4}$

Substitute the value of $y$ to the first equation:

$\rightarrow - 8 x + \left(- \frac{7}{4}\right) = 2$

$\rightarrow - 8 x - \frac{7}{4} = 2$

$\rightarrow \frac{- 32 x - 7}{4} = 2$

$\rightarrow - 32 x - 7 = 4 \cdot 2$

$\rightarrow - 32 x - 7 = 8$

$\rightarrow - 32 x = 8 + 7$

$\rightarrow - 32 x = 15$

$\rightarrow x = - \frac{15}{32}$:)