# How do you solve by elimination 8x + 3y= -9 and -8x + y = 29?

May 13, 2015
• We can Add the two equations to eliminate $x$

$8 x + 3 y = - 9$
$- 8 x + y = 29$
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$\left(\cancel{8 x} + \left(- \cancel{8 x}\right)\right) + \left(3 y + y\right) = - 9 + 29$

$4 y = 20$

Dividing both sides by 4, we get :

$\frac{4 y}{4} = \frac{20}{4}$

$y = 5$

Substituting $y = 5$ in the second equation, we get:

$- 8 x + 5 = 29$

Transposing 5 to the other side we get:

$- 8 x = 29 - 5$

$- 8 x = 24$

Dividing both sides by $- 8$ will give us:

$\frac{- 8 x}{-} 8 = \frac{24}{-} 8$

$x = - 3$

The Solution to the above equations is:

color(green)(x = -3 and y = 5

Substitute these values of $x \mathmr{and} y$ in any of the equations and check if both sides equal each other.