# How do you solve 1/2x+2y=3, 6y+1=x by substitution?

## List item

Dec 9, 2016

I found:
$x = 4$
$y = \frac{1}{2}$

#### Explanation:

Take the $x$ expression from the second equation and substitute into the first:
$\frac{1}{2} \cdot \left(\textcolor{red}{6 y + 1}\right) + 2 y = 3$
rearrange:
$6 y + 1 + 4 y = 6$
$10 y = 5$
$y = \frac{5}{10} = \frac{1}{2}$
go back to the second equation and substitute this value of $y$:
$x = 6 \cdot \textcolor{b l u e}{\frac{1}{2}} + 1 = 3 + 1 = 4$