SOLUTION: solve the following equation by row reducing to echlon form 3x+5y=9 2x+3y=5

Question 1109954: solve the following equation by row reducing to echlon form
3x+5y=9
2x+3y=5
Found 2 solutions by josgarithmetic, greenestamps:
Answer by josgarithmetic(39625) (Show Source): You can put this solution on YOUR website!
If Elimination Method is chosen,

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(That should still help, even if you want Matrix instead, to reduce.)
Answer by greenestamps(13203) (Show Source): You can put this solution on YOUR website!

There are many different possible paths to take in reducing the matrix to row echelon form....

The original matrix A:

First step: make A(1,1)=1.
You could divide row 1 by 3; but that introduces fractions. It is already easy enough, in the Gauss-Jordan elimination process, to make simple arithmetic errors, without introducing fractions. So my choice for making A(1,1)=1 id to replace row 1 with (row 2 - row 1):

Step 2: make A(2,1)=0.
We have no choice here; we need to use the 1 in A(1,1) to make A(2,1) equal to 0. Replace row 2 with (row 2 - 2*row 1):

Step 3: make A(2,2)=1.
This one is simple -- multiply row 2 by -1:

Step 4: make A(1,2)=0.
Again we have no choice but to use the 1 in A(2,2). Replace row 1 with (row 1 - 2*row 2):

The matrix is now in reduced row echelon form.

The solution to the system is x=-2, y=3.
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