Zen F. answered • 04/26/21
Middle and High School Math Tutor
The elimination method for solving linear systems
Another way of solving a linear system is to use the elimination method. In the elimination method you either add or subtract the equations to get an equation in one variable.
When the coefficients of one variable are opposites you add the equations to eliminate a variable and when the coefficients of one variable are equal you subtract the equations to eliminate a variable.
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If you don't have equations where you can eliminate a variable by addition or subtraction you directly you can begin by multiplying one or both of the equations with a constant to obtain an equivalent linear system where you can eliminate one of the variables by addition or subtraction.
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10x + 3y = 67
5x = 2 + 2y
.......rewrite the 2nd equation to get standard form....Ax+By=C
5x-2y = 2 ............... 2nd equation rewritten
10x + 3y = 67
........we need to add or subtract the two equation in order to ELIMINATE one of the variables......
........if you add them now you will not eliminate because the coefficients on the variables don't add to zero....
.......so multiply the 2nd equation by (-2) to get a -10 coefficient value on the x variable like so.....
-10x + 4y = -4
10x + 3y = 67
..........................now we add the two equations together to ELIMINATE the x variable like so.....
0 + 7y = 63 or 7y = 63
y = 63/7=9.....substitute in either equation to find x value..... 10(x) + 3(9) = 67
10x + 27 = 67
10x = 67-27 = 40
x = 4 and y=9.............
check in both equations......
5x=2 + 2y....5(4) = 2+ 2(9) = 20..that checks...
10x + 3y = 67......10(4) + 3(9) = 67.....that checks too.......
we had to use the 2nd condition to modify the 2nd equation to solve the system
