Elimination Method
Steps:
| 1) multiply one or both of the equations by a constant to obtain coefficients that differ only in sign for one of the variables |
| 2) add the revised equation for step one and solve for the remaining variable |
| 3) substitiute the value obtained is step two into one of the orginal equations and solve for the other variable |
Example: Solve the system of equations
10x + y = 25 equation 1
45x + 5y = 10 equation 2
1) multiply equation 1 by -5
10x + y = 25 write equation 1
-50x+ -5y = -125 revised equation 1
2) add the revised equation 1 with equation 2
-50x + -5y = -125 solve
+ 45x + 5y = 10
-5x = -115
x = 23
3) substitute x from step 2 into orginal equation and solve for y
10x + y = 25 write equation 1
10(23) + y = 25 substitute
230 + y = 25 solve
y = 205
the answer is (23,205)