# How do solve the following linear system?: y= -2x + 1 , 8x + 3y= -9 ?

Jan 7, 2016

x = - 6 , y = 13

#### Explanation:

write the equations with labels on them- this helps when wedo operations on them.

y + 2x = 1 (1)
3y + 8x = - 9 (2)

to eliminate y multiply (1) by - 3

(- 3y) - 6x = - 3 (3)

now add (2) and (3 ) and y is eliminated.

2x = - 12 $\Rightarrow x = - 6$

now substitute x = - 6 in (1) ( you could substitute in (2) if you wish )

y + $2 \times \left(- 6\right) = 1 \Rightarrow y - 12 = 1 \Rightarrow y = = 1 + 12 = 13$

check: x= - 6 , y = 13 in (1)→ 13 + 2 (- 6) =13 - 12 =1 and equation is true.

check x = - 6 , y = 13 in (2) →3(13) + 8(- 6 ) = 39 - 48 = - 9 and equation is also true.