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7nadin3 [17]
1 year ago
8

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

Mathematics
1 answer:
ryzh [129]1 year ago
4 0

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.

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

<h3>If you can use an online graphing calculator...</h3>

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

<h3>If you have a physical graphing calculator (like TI-84)</h3>

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

8x-3y=17\\-3y=-8x+17\\y=\frac{8}{3}x-\frac{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

<h3>If you just have graphing paper...</h3>

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

8x-3y=17\\-3y=-8x+17\\y=\frac{8}{3}x-\frac{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.
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