How do you solve 9x-9y=-27 and 5x+27=y using substitution?

Feb 9, 2017

See the entire solution process below:

Explanation:

Step 1) Because the second equation is already solved for $y$, substitute $5 x + 27$ for $y$ in the first equation and solve for $x$:

$9 x - 9 y = - 27$ becomes:

$9 x - 9 \left(5 x + 27\right) = - 27$

$9 x - 45 x - 243 = - 27$

$- 36 x - 243 = - 27$

$- 36 x - 243 + \textcolor{red}{243} = - 27 + \textcolor{red}{243}$

$- 36 x - 0 = 216$

$- 36 x = 216$

$\frac{- 36 x}{\textcolor{red}{- 36}} = \frac{216}{\textcolor{red}{- 36}}$

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{- 36}}} x}{\cancel{\textcolor{red}{- 36}}} = - 6$

$x = - 6$

Step 2) Substitute $- 6$ for $x$ in the second equation and calculate $y$:

$5 x + 27 = y$ becomes:

$\left(5 \times - 6\right) + 27 = y$

$- 30 + 27 = y$

$- 3 = y$

$y = - 3$

The solution is $x = - 6$ and $y = - 3$ or $\left(- 6 , - 3\right)$