# How do you solve the following system?: y= .5x+2 , 2y=4x+3

Feb 13, 2016

Solution is $x = \frac{1}{3} , y = \frac{13}{6}$

#### Explanation:

The equations are $y = 0.5 x + 2$ and $2 y = 4 x + 3$

Multiplying the first equation by $2$ we get

$2 y = x + 4$ but $2 y = 4 x + 3$

Hence $x + 4 = 4 x + 3$ or $3 x = 1$ or $x = \frac{1}{3}$

Putting $x = \frac{1}{3}$ in $y = 0.5 x + 2$

we get $y = 0.5 \cdot \frac{1}{3} + 2 = \frac{1}{6} + 2 = \frac{13}{6}$

Hence solution is $x = \frac{1}{3} , y = \frac{13}{6}$