# How do you solve 4x + 3y = - 4 and 3x - 7y = 34?

Jan 29, 2017

See the entire solution process below:

#### Explanation:

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

$4 x + 3 y = - 4$

$4 x + 3 y - \textcolor{red}{3 y} = - 4 - \textcolor{red}{3 y}$

$4 x + 0 = - 4 - 3 y$

$4 x = - 4 - 3 y$

$\frac{4 x}{\textcolor{red}{4}} = \frac{- 4 - 3 y}{\textcolor{red}{4}}$

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{4}}} x}{\cancel{\textcolor{red}{4}}} = - \frac{4}{4} - \frac{3 y}{4}$

$x = - 1 - \frac{3}{4} y$

Step 2) Substitute $- 1 - \frac{3}{4} y$ for $x$ in the second equation and solve for $y$:

$3 \left(- 1 - \frac{3}{4} y\right) - 7 y = 34$

$- 3 - \frac{9}{4} y - 7 y = 34$

$\textcolor{red}{3} - 3 - \frac{9}{4} y - 7 y = \textcolor{red}{3} + 34$

$- \frac{9}{4} y - 7 y = 37$

$- \frac{9}{4} y - \left(\frac{4}{4} \times 7\right) y = 37$

$- \frac{9}{4} y - \frac{28}{4} y = 37$

$- \frac{37}{4} y = 37$

$- \frac{\textcolor{b l u e}{4}}{\textcolor{red}{37}} \times - \frac{37}{4} y = - \frac{\textcolor{b l u e}{4}}{\textcolor{red}{37}} \times 37$

$\frac{\cancel{- \textcolor{b l u e}{4}}}{\cancel{\textcolor{red}{37}}} \times \frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{- 37}}}}{\textcolor{b l u e}{\cancel{\textcolor{b l a c k}{4}}}} y = - \frac{\textcolor{b l u e}{4}}{\cancel{\textcolor{red}{37}}} \times \textcolor{red}{\cancel{\textcolor{b l a c k}{37}}}$

$y = - 4$

Step 3) Substitute $- 4$ for $y$ in the solution to the first equation at the end of Step 1 and calculate $x$:

$x = - 1 - \left(\frac{3}{4} \times - 4\right)$

$x = - 1 - \left(\frac{3}{\textcolor{red}{\cancel{\textcolor{b l a c k}{4}}}} \times - \textcolor{red}{\cancel{\textcolor{b l a c k}{4}}}\right)$

$x = - 1 - \left(- 3\right)$

$x = - 1 + 3$

$x = 2$

The solution to this problem is:

$x = 2$ and $y = - 4$