Question

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`?

Answer 1

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.

`2x+y=4 \Leftrightarrow y = -2x + 4`

`x+y=3 \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 `(1,2)`. Since we graphed these on the same set of axes, the intersections implies that `(1,2)` is a solution to both equations.

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