MATHEMATICS
ALGEBRA
Solving Systems of Equations with the Addition Method
Suppose you have are confronted with the following problem:
Solve the system:
x + y = 8
4x - 2y = 8
There are four steps involved in solving a problem like this:
Multiply so that the coefficients of the x or of the y cancel out
Add the equations
Solve the equation derived from step 2.
Substitute the answer from step into one of the original equations. Then solve for the remaining variable:
So, based on the above steps, the first thing I will do is multiply the first equation by 2:
2( x+y = 8)
2x + 2y = 16
Next I will add the two equations:
2x + 2y = 16
4x - 2y = 8
Notice that the 2y and the -2y cancel each other out:
6x = 24
Divide both sides by 6 and we have:
x = 4
Now substitute the derived value for x back into one of the original equations. I will pick the first one because it is the simplest:
6 + y = 8
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y = 8 - 6
y = 2
Therefore, the solution is: x = 6 and y = 2, or (6,2)