# How do you solve 2x+3y=6 and 2x-y=-2 using substitution?

Apr 5, 2017

$\left(0 , 2\right)$

#### Explanation:

To solve by $\textcolor{b l u e}{\text{substitution}}$

Rearrange one of the equations in terms of x or y then substitute into the other equation and solve for x or y

$2 x - y = - 2 \to \left(1\right)$

$2 x + 3 y = 6 \to \left(2\right)$

Rearrange ( 1 ) to obtain y in terms of x , avoiding the use of fractions.

$\Rightarrow y = 2 x + 2 \to \left(3\right)$

$\textcolor{b l u e}{\text{Substitute }}$ into equation ( 2 )

$2 x + 3 \left(\textcolor{red}{2 x + 2}\right) = 6 \leftarrow \textcolor{red}{\text{ and solve for x}}$

$\Rightarrow 2 x + 6 x + 6 = 6$

$\Rightarrow 8 x + 6 = 6$

subtract 6 from both sides.

$8 x \cancel{+ 6} \cancel{- 6} = 6 - 6$

$\Rightarrow 8 x = 0 \Rightarrow x = 0$

Substitute this value into ( 3 ) and evaluate for y

$x = 0 \to y = 0 + 2 = 2$

$\Rightarrow \text{point of intersection } = \left(0 , 2\right)$
graph{(y-2x-2)(y+2/3x-2)=0 [-10, 10, -5, 5]}