How do you solve 9x+7y = -65 and x= -1-7y using substitution?

Mar 26, 2016

Given
[1]$\textcolor{w h i t e}{\text{XXX}} 9 x + 7 y = - 65$
[2]$\textcolor{w h i t e}{\text{XXX}} x = - 1 - 7 y$

By substitution
Substituting $\left(- 1 - 7 y\right)$ from [2] into [1] for $x$
[3]$\textcolor{w h i t e}{\text{XXX}} 9 \left(- 1 - 7 y\right) + 7 y = - 65$
Simplifying
[4]$\textcolor{w h i t e}{\text{XXX}} - 9 - 63 y + 7 y = - 65$

[5]$\textcolor{w h i t e}{\text{XXX}} - 56 y = - 56$

[6]$\textcolor{w h i t e}{\text{XXX}} y = 1$

Substituting $1$ from [6] into [2] for $y$
[7]$\textcolor{w h i t e}{\text{XXX}} x = - 1 - 7 \left(1\right)$
Simplifying
[8]$\textcolor{w h i t e}{\text{XXX}} x = - 8$

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Verify by substituting $\left(x , y\right) = \left(- 8 , 1\right)$ into equation [1]