How do you solve the system of equations -4x + 4y = 4 and y = 9x + 73?

Mar 20, 2018

See a solution process below:

Explanation:

Step 1) Solve the first equation for $x$:

$- 4 x + 4 y = 4$

$- 4 x + 4 y - \textcolor{red}{4 y} = 4 - \textcolor{red}{4 y}$

$- 4 x + 0 = 4 - 4 y$

$- 4 x = 4 - 4 y$

$\frac{- 4 x}{\textcolor{red}{- 4}} = \frac{4 - 4 y}{\textcolor{red}{- 4}}$

$x = \frac{4}{\textcolor{red}{- 4}} - \frac{4 y}{\textcolor{red}{- 4}}$

$x = - 1 + y$

Step 2) Substitute $\left(- 1 + y\right)$ for $x$ in the second equation and solve for $y$:

$y = 9 x + 73$ becomes:

$y = 9 \left(- 1 + y\right) + 73$

$y = \left(9 \cdot - 1\right) + \left(9 \cdot y\right) + 73$

$y = - 9 + 9 y + 73$

$y - \textcolor{red}{9 y} = - 9 + 9 y - \textcolor{red}{9 y} + 73$

$1 y - \textcolor{red}{9 y} = - 9 + 0 + 73$

$\left(1 - \textcolor{red}{9}\right) y = - 9 + 73$

$- 8 y = 64$

$\frac{- 8 y}{\textcolor{red}{- 8}} = \frac{64}{\textcolor{red}{- 8}}$

$y = - 8$

Step 3) Substitute $- 8$ for $y$ in the solution to the first equation at the end of Step 1 and calculate $x$:

$x = - 1 + y$ becomes:

$x = - 1 + \left(- 8\right)$

$x = - 1 - 8$

$x = - 9$

The Solution Is:

$x = - 9$ and $y = - 8$

Or

$\left(- 9 , - 8\right)$