# How do you solve the system of equations by graphing and then classify the system as consistent or inconsistent 2x+ y = 4, x + y =3?

##### 1 Answer
Dec 26, 2017

Graph both equations on the same set of axes to see if there is a point of intersection. If there is, then there is at least one solution and it is consistent; otherwise it is inconsistent.

#### Explanation:

Graph both equations on the same set of axes to see if there is a point of intersection.

$2 x + y = 4 \setminus \Leftrightarrow y = - 2 x + 4$

$x + y = 3 \setminus \Leftrightarrow y = - x + 3$

graph{(y-(-2x+4))(y-(-x+3))=0 [-1.882, 4.277, -0.307, 2.77]}

There is a solution at $\left(1 , 2\right)$. Since we graphed these on the same set of axes, the intersections implies that $\left(1 , 2\right)$ is a solution to both equations.

Since there is at least one solution, this is consistent.