# How do you solve -2x+3y=15 and -6x+6y=18 using substitution?

Mar 28, 2018

See a solution process below:

#### Explanation:

Step 1) Solve the second equation for $y$:

$- 6 x + 6 y = 18$

$\frac{- 6 x + 6 y}{\textcolor{red}{6}} = \frac{18}{\textcolor{red}{6}}$

$\frac{- 6 x}{\textcolor{red}{6}} + \frac{6 y}{\textcolor{red}{6}} = 3$

$- x + y = 3$

$- x + \textcolor{red}{x} + y = 3 + \textcolor{red}{x}$

$0 + y = 3 + x$

$y = 3 + x$

Step 2) Substitute $\left(3 + x\right)$ for $y$ in the first equation and solve for $x$:

$- 2 x + 3 y = 15$ becomes:

$- 2 x + 3 \left(3 + x\right) = 15$

$- 2 x + \left(3 \times 3\right) + \left(3 \times x\right) = 15$

$- 2 x + 9 + 3 x = 15$

$- 2 x + 9 - \textcolor{red}{9} + 3 x = 15 - \textcolor{red}{9}$

$- 2 x + 0 + 3 x = 6$

$- 2 x + 3 x = 6$

$\left(- 2 + 3\right) x = 6$

$1 x = 6$

$x = 6$

Step 3) Substitute $6$ for $x$ in the solution to the second equation at the end of Step 1 and calculate $y$:

$y = 3 + x$ becomes:

$y = 3 + 6$

$y = 9$

The Solution Is:

$x = 6$ and $y = 9$

Or

$\left(6 , 9\right)$