SOLUTION: 2x+y=9 -3x+2y=4

Question 120624: 2x+y=9
-3x+2y=4
Answer by nabla(475) (Show Source): You can put this solution on YOUR website!
Solve the first equation for y:

Substitute this y into the second equation:

Combine terms on the left, subtract 19 from both sides
Divide both sides by -7.
Now, substitute this value of x into the first equation where we solved for y in terms of x: .
This gives the solution set S:{2,5}.

Additionally, we could solve this system through techniques of linear algebra as follows:
Matrix:
|2 1 9|
|-3 2 4|
(3/2)R1+R2->
|2 1 9|
|0 7/2 35/2|
(1/2)R1->
|1 1/2 9/2|
|0 7/2 35/2|
(2/7)R2->
|1 1/2 9/2|
|0 1 5 |
-1/2R2+R1->
|1 0 2 |
|0 1 5 |
Making S={2,5} the only solution.
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