# How do you solve 6x+9y=3 and x+4y=-2?

May 23, 2018

See a solution process below:

#### Explanation:

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

$x + 4 y = - 2$

$x + 4 y - \textcolor{red}{4 y} = - 2 - \textcolor{red}{4 y}$

$x + 0 = - 2 - 4 y$

$x = - 2 - 4 y$

Step 2) Substitute $\left(- 2 - 4 y\right)$ for $x$ in the first equation and solve for $y$:

$6 x + 9 y = 3$ becomes:

$6 \left(- 2 - 4 y\right) + 9 y = 3$

$\left(6 \times - 2\right) - \left(6 \times 4 y\right) + 9 y = 3$

$- 12 - 24 y + 9 y = 3$

$- 12 + \left(- 24 + 9\right) y = 3$

$- 12 + \left(- 15\right) y = 3$

$- 12 - 15 y = 3$

$- 12 + \textcolor{red}{12} - 15 y = 3 + \textcolor{red}{12}$

$0 - 15 y = 15$

$- 15 y = 15$

$\frac{- 15 y}{\textcolor{red}{- 15}} = \frac{15}{\textcolor{red}{- 15}}$

$y = - 1$

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

$x = - 2 - 4 y$ becomes:

$x = - 2 - \left(4 \times - 1\right)$

$x = - 2 - \left(- 4\right)$

$x = - 2 + 4$

$x = 2$

The Solution Is:

$x = 2$ and $y = - 1$

Or

$\left(2 , - 1\right)$