# How do you solve 2x + y = 5, 3x - y =10 by graphing and classify the system?

Dec 4, 2017

See explanation.

#### Explanation:

To solve the system of equations by graphing you have to plot the two graphs on a single coordinate plane and see if the graphs:

• have no common points (are two parallel disjoint lines)

• have infinitely many common points (two functions are the same line)

• have exactly one common point

Here we can see:

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

As we can see the graphs intersect in (3;-1), so the values $x = 3 , y = - 1$ are the only solution of the system.