# How do you solve the system of equations y= x + 2 and y = 5x + 5?

Mar 10, 2017

$\left(- \frac{3}{4} , \frac{5}{4}\right)$

#### Explanation:

Since both equations are expressed in terms of y we can equate the right sides.

$\Rightarrow 5 x + 5 = x + 2 \leftarrow \text{ solve for x}$

subtract x from both sides.

$5 x - x + 5 = \cancel{x} \cancel{- x} + 2$

$\Rightarrow 4 x + 5 = 2$

subtract 5 from both sides.

$4 x \cancel{+ 5} \cancel{- 5} = 2 - 5$

$\Rightarrow 4 x = - 3$

divide both sides by 4

$\frac{\cancel{4} x}{\cancel{4}} = \frac{- 3}{4}$

$\Rightarrow x = - \frac{3}{4}$

Substitute this value into either of the 2 equations to obtain y

$\text{Using } y = x + 2$

$x = - \frac{3}{4} \to y = - \frac{3}{4} + 2 = \frac{5}{4}$

$\text{the solution is } \left(- \frac{3}{4} , \frac{5}{4}\right)$
graph{(y-x-2)(y-5x-5)=0 [-10, 10, -5, 5]}