# How do you solve the following system: 5x+y=-7, 6x + 7y = -9 ?

Jul 2, 2017

See a solution process below:

#### Explanation:

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

$5 x + y = - 7$

$- \textcolor{red}{5 x} + 5 x + y = - \textcolor{red}{5 x} - 7$

$0 + y = - 5 x - 7$

$y = - 5 x - 7$

Step 2) Substitute $\left(- 5 x - 7\right)$ for $y$ in the second equation and solve for $x$:

$6 x + 7 y = - 9$ becomes:

$6 x + 7 \left(- 5 x - 7\right) = - 9$

$6 x + \left(7 \cdot - 5 x\right) - \left(7 \cdot 7\right) = - 9$

$6 x + \left(- 35 x\right) - 49 = - 9$

$6 x - 35 x - 49 = - 9$

$\left(6 - 35\right) x - 49 = - 9$

$- 29 x - 49 = - 9$

$- 29 x - 49 + \textcolor{red}{49} = - 9 + \textcolor{red}{49}$

$- 29 x - 0 = 40$

$- 29 x = 40$

$\frac{- 29 x}{\textcolor{red}{- 29}} = \frac{40}{\textcolor{red}{- 29}}$

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{- 29}}} x}{\cancel{\textcolor{red}{- 29}}} = - \frac{40}{29}$

$x = - \frac{40}{29}$

Step 3) Substitute $- \frac{40}{29}$ for $x$ in the solution to the first equation at the end of Step 1 and calculate $y$:

$y = - 5 x - 7$ becomes:

$y = \left(- 5 \times - \frac{40}{29}\right) - 7$

$y = \frac{200}{29} - 7$

$y = \frac{200}{29} - \left(\frac{29}{29} \times 7\right)$

$y = \frac{200}{29} - \frac{203}{29}$

$y = - \frac{3}{29}$

The solution is: $x = - \frac{40}{29}$ and $y = - \frac{3}{29}$ or $\left(- \frac{40}{29} , - \frac{3}{29}\right)$