Question

Hey can someone tell me the steps to solving a system of equations with graphing

Answer 1

Let's go through the following example to show how to solve a system of equations by graphing. I won't solve this system, I will just show how to.

`8x-3y = 17\\4x+y=21`

If you can use an online graphing calculator...

If you have an online grapher (like Desmos) at your disposal, then you can put each equation in it as it is.

• Lines intersect -> Put your cursor over the point of intersection to get the solution.
• Lines never intersect -> The lines are parallel and there is no solution
• Lines perfectly fall on each other -> The lines are the same and have infinite solutions

If you have a physical graphing calculator (like TI-84)

1. Get both equations in the form
`y=mx+b` by solving for y.

`8x-3y=17\\-3y=-8x+17\\y=(8)/(3)x-(17)/(3)`
`4x+y=21\\y=-4x+21`

2. Put both equations in the graphing calculator

• Lines intersect -> Find the intersection point using your graphing calculator's mechanics (each one is a little different)
• Lines never intersect -> The lines are parallel and there is no solution
• Lines perfectly fall on each other -> The lines have the same equation and have infinite solutions

If you just have graphing paper...

1. Get both equations into the form
`y=mx+b` by solving for y.

`8x-3y=17\\-3y=-8x+17\\y=(8)/(3)x-(17)/(3)`
`4x+y=21\\y=-4x+21`

2. Plug in a few different points for x and calculate their y-values.

3. Plot those points on the graph paper

• Lines intersect -> Find the intersection point's coordinates to get the solution for x and y.
• Lines never intersect -> The lines are parallel and there is no solution
• Lines perfectly fall on each other -> The lines have the same equation and have infinite solutions.