# How do you solve 2x+3y=21 and -3x-6y=-24?

Feb 26, 2017

See the entire solution process below:

#### Explanation:

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

$- 3 x - 6 y = - 24$

$- 3 x - 6 y + \textcolor{red}{6 y} = - 24 + \textcolor{red}{6 y}$

$- 3 x - 0 = - 24 + 6 y$

$- 3 x = - 24 + 6 y$

$\frac{- 3 x}{\textcolor{red}{- 3}} = \frac{- 24 + 6 y}{\textcolor{red}{- 3}}$

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{- 3}}} x}{\cancel{\textcolor{red}{- 3}}} = \frac{- 24}{\textcolor{red}{- 3}} + \frac{6 y}{\textcolor{red}{- 3}}$

$x = 8 - 2 y$

Step 2) Substitute $8 - 2 y$ for $x$ in the first equation and solve for $y$:

$2 x + 3 y = 21$ becomes:

$2 \left(8 - 2 y\right) + 3 y = 21$

$\left(2 \times 8\right) - \left(2 \times 2 y\right) + 3 y = 21$

$16 - 4 y + 3 y = 21$

$16 + \left(- 4 + 3\right) y = 21$

$16 - y = 21$

$16 - y - \textcolor{red}{16} = 21 - \textcolor{red}{16}$

$16 - \textcolor{red}{16} - y = 5$

$0 - y = 5$

$- y = 5$

$- 1 \times - y = - 1 \times 5$

$y = - 5$

Step 3) Substitute $- 5$ for $y$ in the solution to the second equation at the end of Step 1 and calculate $x$:

$x = 8 - 2 y$ becomes:

$x = 8 - \left(2 \times - 5\right)$

$x = 8 - \left(- 10\right)$

$x = 8 + 10$

$x = 18$

The solution is: $x = 18$ and $y = - 5$ or $\left(18 , - 5\right)$