Question

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

Answer 1

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.