SOLUTION: Solve by the elimination method. 5x-y=26 x+2y=25 What is the solution of the system?

Question 314629: Solve by the elimination method.
5x-y=26
x+2y=25
What is the solution of the system?
Found 2 solutions by Fombitz, rapaljer:
Answer by Fombitz(32388) (Show Source): You can put this solution on YOUR website!
1.
2.
Multiply eq. 1 by 2 and add to eq. 2,

Then from eq. 1,

.
.
.

Answer by rapaljer(4671) (Show Source): You can put this solution on YOUR website!
Multiply both sides of the first equation by 2, so when you add the two equations together, the y terms will subtract out.
10x-2y = 52
x+2y = 25

When you add these together, you get
11x =77
x=7

Substitute x=7 into the first equation:
5x-y=26
5(7)-y=26
35-y=26
-y=26-35
-y=-9
y=9

Check in the other equation
x+2y=25
7+2(9)=25
7+18=25

For additional explanation on this topic, please see my own website. Click on my tutor name "rapaljer" and then click on the link that is given there. From my Homepage, look for the link "Basic, Intermediate, and College Algebra: One Step at a Time." Select "Basic Algebra," and look for "Chapter 4", Section 4.07 Systems of Equations." These sections include my own explanation written especially for students who may have trouble understanding these skills, examples, exercises, and ALL the answers. Many of the exercises are solved in detail on the "Math in Living Color" pages that go with these pages.

Dr. Robert J. Rapalje, Retired
Seminole State College of Florida
Altamonte Springs Campus
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