# How do solve the following linear system?:  -x-7y=14 , x-2y=8 ?

Apr 2, 2016

$\left(x , y\right) = \left(\frac{28}{9} , - \frac{22}{9}\right)$

#### Explanation:

Solve by elimination and substitution

color(blue)(-x-7y=14

color(blue)(x-2y=8

We can eliminate $x$ in the first equation by $- x$ in the second equation

$\rightarrow \left(- x - 7 y = 14\right) + \left(x - 2 y = 8\right)$

$\rightarrow - 9 y = 22$

color(green)(rArry=-22/9

Substitute the value of $y$ to the second equation

$\rightarrow x - 2 \left(- \frac{22}{9}\right) = 8$

$\rightarrow x + \frac{44}{9} = 8$

color(green)(rArrx=8-44/9=28/9

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Check ($- x - 7 y = 14$)

$\rightarrow - \frac{28}{9} - 7 \left(- \frac{22}{9}\right) = 14$

$\rightarrow - \frac{28}{9} + \frac{154}{9} = 14$

$\rightarrow \frac{- 28 + 154}{9} = 14$

$\rightarrow \frac{126}{9} = 14$

color(orange)(rArr14=14

$\approx \approx \approx \approx \approx \approx \approx \approx \approx \approx \approx \approx \approx \approx \approx \approx \approx$

Check ($x - 2 y = 8$)

$\rightarrow \frac{28}{9} - 2 \left(- \frac{22}{9}\right) = 8$

$\rightarrow \frac{28}{9} + \frac{44}{9} = 8$

$\rightarrow \frac{28 + 44}{9} = 8$

$\rightarrow \frac{72}{9} = 8$

color(violet)(rArr8=8

$\approx \approx \approx \approx \approx \approx \approx \approx \approx \approx \approx \approx \approx \approx \approx \approx \approx$

:. color(blue)( ul bar |(x,y)=28/9,-22/9|