# How do you solve y=2x-3 and y=-3x+2 using substitution?

May 18, 2016

The solution for the system of equations is:

color(green)(x =1
color(green)(y = - 1

#### Explanation:

color(blue)(y = 2x - 3 ............equation $\left(1\right)$

$y = - 3 x + 2$......equation $\left(2\right)$

Solving by substitution.

Substituting equation $1$ in equation $2$:

$y = - 3 x + 2$

$\textcolor{b l u e}{2 x - 3} = - 3 x + 2$

$2 x + 3 x = 2 + 3$

$5 x = 5$

$x = \frac{5}{5}$

color(green)(x =1

Finding the value of $y$ from equation $1 :$

$y = 2 x - 3$

$y = \left(2 \cdot 1\right) - 3$

$y = 2 - 3$

color(green)(y = - 1