# How do you solve the system of equations by graphing and then classify the system as consistent or inconsistent y = x + 2 and y = –x – 3?

Jun 24, 2018

See a solution process below:

#### Explanation:

First, we need to graph each equation by solving each equation for two points and then drawing a straight line through the two points.

Equation 1:

First Point: For $x = 0$

$y = 0 + 2$

$y = 2$ or $\left(0 , 2\right)$

Second Point: For $x = 2$

$y = 2 + 2$

$y = 4$ or $\left(2 , 4\right)$

graph{(y - x - 2)(x^2+(y-2)^2-0.075)((x-2)^2+(y-4)^2-0.075)=0 [-15, 15, -10, 5]}

Equation 2:

First Point: For $x = 0$

$y = - 0 - 3$

$y = - 3$ or $\left(0 , - 3\right)$

Second Point: For $x = 3$

$y = - 3 - 3$

$y = - 6$ or $\left(3 , - 6\right)$

graph{(y + x + 3)(y - x - 2)(x^2+(y+3)^2-0.075)((x-3)^2+(y+6)^2-0.075)=0 [-15, 15, -10, 5]}

From the graphs we can see the line intersects at: $\left(\textcolor{red}{- 2.5} , \textcolor{red}{- 0.5}\right)$

graph{(y + x + 3)(y - x - 2)((x+2.5)^2+(y+0.5)^2-0.075)=0 [-15, 15, -10, 5]}

By definition: a consistent system has at least one solution

Therefore, this system of equations is consistent