System of Equations

Sydney A

Elimination - 500

1. Put into slope intercept.

2. Multiply the equation that makes one variable ready to be eliminated.

3. Add equations.

4. Plug in y.

5. Solve for x.


It's best to use elimination when two of the same variables have the same co-efficient.

Substitution - 500

Below is the video on how to use substitution.

It's best to use substitution when the coefficient of any variable is 1.

Graphing - 500

It's best to use graphing when your equations are in slope intercept form. Because it's really easy to find slope and y-intercept when your equations are in slope-intercept form. To solve a system of equations with graphing, you simplify your equations to slope intercept form, and then take the slope and do rise over run to find your intersection point. When simplified to slope intercept form, y= -2/7x + 2 and y= -5/7x -1 were the equations. The intersection point is (-7,4).

Word Problems - 500

All you have to do is find the equations in the scenario. Once you have the equations, just solve it! When one customer rented a floor sander for 4 hrs and paid $63, and someone else rented for 6 hrs. and paid $87, those are your two equations!

(x+4y=63 and x+6y=87) Now, just choose your method. Since the 'x's are the same, I'm going to use elimination.

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Write a System - 500

Below is the video on how to solve a write a system. *hint: that's what you do! You write your systems.

The 3 types of Solutions

One Solution

This is the most common solution. When you get one solution, you have found the intersection point for your two lines. You write them as an ordered pair. (x,y)

No Solution

No solution is one of the two special cases out of these three possible outcomes. It is when your two lines are parallel, meaning they they have the same slope and a different y-intercept. If they have the same slope and a different y-intercept, then the two lines are parallel, and therefore will never intersect, which means there is no solution.


Take for example, y=5x-2 and y=5x+4 . They have the same slope a different y-int. They will never cross. They are parallel. This is a no solution.

Infinitely Many

Infinitely many is the other special case. But this is when the two equations simplify to be the exact same line. This will be when your y-intercept and your slope are the same. Your two lines, will then be on top of each other, and then every single point will be an intersection point. They are infinitely crosses, hence, there will be infinitely many solutions.