# How do you solve the system of linear equations x + 3y = 5 and 2x - y = 5?

May 30, 2018

$\frac{20}{7} = x$, $\frac{5}{7} = y$

#### Explanation:

$x + 3 y = 5$

$2 x - y = 5$

If both equations equal $5$, we can set them equal to eachother

$x + 3 y = 2 x - y$

$4 y = x$

Now we can substitute $4 y$ for $x$ in one of the equations (let's pick the first one)

$4 y + 3 y = 5$

$7 y = 5$

$y = \frac{5}{7}$

Now, if $4 y = x$, then $4 \times \frac{5}{7} = x$ or $x = \frac{20}{7}$

Now to check our work. Let's substitute $\frac{5}{7}$ and $\frac{20}{7}$ for $y$ and $x$ in the second equation. If we have the correct answers, our equation should still equal $5$.

$2 \left(\frac{20}{7}\right) - \frac{5}{7}$

$\frac{40}{7} - \frac{5}{7}$

$\frac{35}{7}$, which simplifies to $5$! So we were correct.