How to Eliminate
What must you do before you add or subtract your equations?
Line up your terms / check if you will eliminate a term / Multiply your equation if needed
Multiply 2x + 8y = 4 by 3
6x + 24y = 12
What should you multiply the top equation by so the x value will be eliminated when you add?
3x + 298y = 999
-6x - 654y = 0
2
Use the elimination method to find the solution to the system of equations:
5x + y = 11
-5x + 4y = 19
x = 1
y = 6
2x-3y =0
-4x +2y = -8
Find x if y=2.
x=3
How can you check your solution?
Plug it back into both original equations and get true statements.
Multiply 4x - 6y = 1 by 7
28x -42y = 7
What should you multiply the top equation by so the y value will be eliminated when you add?
554x -5y = 420
345x + 20y = 69
4
Use the elimination method to find the solution to the system of equations:
10x - 10y = 10
-5x + 20y =25
x = 3
y = 2
2x+3y=9
x+4y=2
Is (6,-1) a solution to the system above?
Yes
After you have found one of the variables what is the next step.
Solve for the remaining variable
Multiply 3x + 3y = 8 by 5
15x + 15y = 40
What should you multiply the top equation by so the x value will be eliminated when you add?
3x + 7083y = 666
18x + 2023y = 1234567
-6
Use the elimination method to find the solution to the system of equations:
5x - 6y = 11
3x + 2y = 29
x = 7
y = 4
When solving, if you get an answer that looks like:
2 = 2
What is the solution?
infinite solutions
When using the elimination method what are you trying to find (what will your answer be?)
The solution to the system
Multiply 10x + 4y = 3 by -2
-20x - 8y = -6
What should you multiply the top equation by so the y value will be eliminated when you add?
88x - 5y = 0
54x + 5y = 12
Nothing
Use the elimination method to find the solution to the system of equations:
2x + 2y = 22
-4x + 10y = -2
x = 8
y = 3
-2x = -3y+16
-2x+3y = 16
OR
2x-3y = -16
What do you do if your equations will not eliminate if you were to add or subtract them?
Multiply an equation by a number so that they will eliminate
Multiply 7x + 9y = 3 by -1
-7x - 9y = -3
What should you multiply the bottom equation by so the y value will be eliminated when you add?
y= 3x +18
y= -5x +6
-1
Use the elimination method to find the solution to the system of equations:
8x + 5y = 26
-8x + 10x = -4
x = 2
y = 2
Rearrange the equation into standard form:
y=2x-14
-2x+y= -14
OR
2x-y = 14