Question

How do you solve the system of equations by graphing and then classify the system as consistent or inconsistent `5x+2y=-15` and `y=2x-12`?

Answer 1

The system is consistent and has the solution:

`x=1, y=-10`.

Explanation:

We have:

`5x+2y = -15`
`y=2x-12`

A System of Equations is Consistent if the system has at least one solution. Graphically this means the equations of the lines the equations represent meet

We can plot the graphs on the same axis:

graph{(5x+2y +15)(y-2x+12)=0 [-10, 10, -15, 15]}

From which it would "appear" that we have a solution:

`x=1, y=-10`,

Where the two lines meet. We can readily verify the system does indeed satisfy both equations.,

Hence, the system is consistent and has the solution:

`x=1, y=-10`.