Expert: Scott A Wilson - 2/16/2011

Question
5x-2y=4
x+2y=8

-3x+2y=11
3x+y=-19

Answer
For 5x-2y=4 and x+2y=8, add them together.  This gives 6x = 12.
When both sides are divided by 6, the result is x = 2.
When this x=2 is put into either equation, y can be found.
We have 10 - 2y = 4 and 2 + 2y = 8.
Both equations gives us 2y = 6, so y = 3.


When -3x+2y=11 and 3x+y=-19 are added together, -3x + 3x cancel, givng 3y = -8.
Dividing by 3 gives y = -8/3.
Putting that back in gives -3x - 16/3 = 11 and 3x - 8/3 = -19.

Adding 16/3 to both sides on the 1st equation gives -3x = 49/3.
Adding 8/3 to both sides on the 2nd equation gives 3x = -49/3.
Both gives x = -49/9.

Takikng x = -49/9 and y = -8/3, put them back in to both equations.
For the 1st equation, this gives 49/3 - 16/3 = 33/3 = 11, which is correct.
For the 2nd equation, this gives -49/3 - 8/3 = -57/3 = -19, and that is also correct.