# How do you solve the following system?: x +12y = 13 , 5x - 2y = -4

Feb 3, 2016

$\left(\frac{3}{2} , \frac{23}{4}\right)$

#### Explanation:

Because this question is in the section for using the Substitution method of solving systems of equations, that is the method I am going to use.

So, we start off with the equations:

$x + 12 y = 13$
$5 x - 2 y = - 4$

1) Set an equation equal to a variable

Since the first equation has a lone variable, on without a coefficient, I'm going to use that one, but you can use whichever one you want.

$x + 12 y = 13$
$\textcolor{red}{12 -} x + 12 y = 13 \textcolor{red}{- 12}$
$\cancel{\textcolor{red}{12 y -}} x \cancel{+ 12 y} = 13 \textcolor{red}{- 12 y}$
color(blue)(x=13-2y

2) Substitute the new equation into the other one

$5 x - 2 y = - 4$
color(blue)(x=13-2y
$5 \left(\textcolor{b l u e}{13 - 2 y}\right) - 2 y = - 4$
$65 - 10 y - 2 y = - 4$
$65 - 12 y = - 4$
$\textcolor{red}{65 -} 65 - 12 y = - 4 \textcolor{red}{- 65}$
$\cancel{\textcolor{red}{65 -} 65} - 12 y = - 4 \textcolor{red}{- 65}$
$- 12 y = - 69$
$\frac{- 12 y = - 69}{\textcolor{red}{- 12}}$
$y = \textcolor{g r e e n}{5.75}$ or y=color(green)(23/4

3) Plug answer back into original equation

$x = 13 - 2 y$
$x = 13 - 2 \left(\textcolor{g r e e n}{5.75}\right)$
$x = 13 - 11.5$
$x = \textcolor{\mathmr{and} a n \ge}{1.5}$ or y=color(orange)(3/2

4) Write the solution as a coordinate (x,y)

The solution is: $\left(\textcolor{\mathmr{and} a n \ge}{\frac{3}{2}} , \textcolor{g r e e n}{\frac{23}{4}}\right)$