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

Mar 3, 2016

The solution for the system of equations is:
color(blue)(x=1
color(blue)(y=1

#### Explanation:

$2 x + y = 3$, multiplying by $2$
$4 x + \textcolor{b l u e}{2 y} = 6$.......equation $\left(1\right)$

$5 x - \textcolor{b l u e}{2 y} = 3$........equation $\left(2\right)$

Solving by elimination

Adding equations $\left(2\right)$ and $\left(1\right)$ results in elimination of color(blue)(2y

$4 x + \cancel{\textcolor{b l u e}{2 y}} = 6$

$5 x - \cancel{\textcolor{b l u e}{2 y}} = 3$

$9 x = 9$

$x = \frac{9}{9}$

color(blue)(x=1

Finding $y$ from equation $1$:
$2 x + y = 3$

$y = 3 - 2 x$

$y = 3 - 2 \times 1$

$y = 3 - 2$

color(blue)(y=1