# How do you solve the following system: x + 8y = 15 , 5x - 7y = 12 ?

May 23, 2018

See a solution process below:

#### Explanation:

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

$x + 8 y = 15$

$x + 8 y - \textcolor{red}{8 y} = 15 - \textcolor{red}{8 y}$

$x + 0 = 15 - 8 y$

$x = 15 - 8 y$

Step 2) Substitute $\left(15 - 8 y\right)$ for $x$ in the second equation and solve for $y$:

$5 x - 7 y = 12$ becomes:

$5 \left(15 - 8 y\right) - 7 y = 12$

$\left(5 \times 15\right) - \left(5 \times 8 y\right) - 7 y = 12$

$75 - 40 y - 7 y = 12$

$75 + \left(- 40 - 7\right) y = 12$

$75 + \left(- 47\right) y = 12$

$75 - 47 y = 12$

$75 - \textcolor{red}{75} - 47 y = 12 - \textcolor{red}{75}$

$0 - 47 y = - 63$

$- 47 y = - 63$

$\frac{- 47 y}{\textcolor{red}{- 47}} = - \frac{63}{\textcolor{red}{- 47}}$

$y = \frac{63}{47}$

Step 3) Substitute $\frac{63}{47}$ for $y$ in the solution to the first equation at the end of Step 1 and calculate $x$:

$x = 15 - 8 y$ becomes:

$x = 15 - \left(8 \times \frac{63}{47}\right)$

$x = 15 - \frac{504}{47}$

$x = \left(\frac{47}{47} \times 15\right) - \frac{504}{47}$

$x = \frac{705}{47} - \frac{504}{47}$

$x = \frac{201}{47}$

The Solution Is:

$x = \frac{201}{47}$ and $y = \frac{63}{47}$

Or

$\left(\frac{201}{47} , \frac{63}{47}\right)$