# How do you solve the system of linear equations y=2x+3, -2x+y=1?

Sep 17, 2017

#### Answer:

$\text{no solution}$

#### Explanation:

$\text{if we consider the 2 equations in "color(blue)"slope-intercept form}$

•color(white)(x)y=mx+b

$\text{where m is the slope and b the y-intercept}$

$- 2 x + y = 1 \to y = 2 x + 1 \Rightarrow m = 2$

$y = 2 x + 3 \Rightarrow m = 2$

$\text{the 2 lines have the same slope and are therefore }$
$\textcolor{b l u e}{\text{parallel}}$

$\text{hence no point of intersection thus no solution}$
graph{(y-2x-3)(y-2x-1)=0 [-10, 10, -5, 5]}