Answer:
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.
[tex]8x-3y = 17\\4x+y=21[/tex]
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 [tex]y=mx+b[/tex] by solving for y.
[tex]8x-3y=17\\-3y=-8x+17\\y=\frac{8}{3}x-\frac{17}{3}[/tex] [tex]4x+y=21\\y=-4x+21[/tex]
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 [tex]y=mx+b[/tex] by solving for y.
[tex]8x-3y=17\\-3y=-8x+17\\y=\frac{8}{3}x-\frac{17}{3}[/tex] [tex]4x+y=21\\y=-4x+21[/tex]
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.
