# How do you determine the solution in terms of a system of linear equations for 1/2x = 4y, 5y - x = -3?

Sep 25, 2015

$x = 8$
$y = 1$

#### Explanation:

I think the easiest method for solving this system is through substitution.

So we are given two equations:
$\frac{1}{2} x = 4 y$
5y−x=−3

Let's get the value of $x$ in the first equation:
$\frac{1}{2} x = 4 y$
$\left(2\right) \left(\frac{1}{2} x\right) = \left(2\right) \left(4 y\right)$
$\textcolor{b l u e}{x = 8 y}$

Now let's substitute this into the second equation:
5y−color(blue)(x)=−3
5y−color(blue)((8y))=−3
-3y=−3
(-1/3)(-3y)=(-1/3)(−3)
(-1/3)(-3y)=(-1/3)(−3)
$\textcolor{red}{y = 1}$

Now that we know the $y$ value, we can solve for the $x$ value:
$\textcolor{b l u e}{x = 8} \textcolor{red}{y}$
$\textcolor{b l u e}{x = 8} \textcolor{red}{\left(1\right)}$
$\textcolor{b l u e}{x = 8}$

So the solution of the system is:
$\textcolor{b l u e}{x = 8}$
$\textcolor{red}{y = 1}$