SOLUTION: My son is supposed to use reduction method to solve the system of equations. Can you please help in explaining the process using this problem? This is from a worksheet. Thank you.

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Question 136249: My son is supposed to use reduction method to solve the system of equations. Can you please help in explaining the process using this problem? This is from a worksheet. Thank you.
{2x - y -7 = 0
{3x + y = 8

Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!
First step is to put the first equation into standard form:

2x-y=7

Now put the coefficients and constants into an augmented matrix:

%28matrix%282%2C3%2C2%2C-1%2C7%2C3%2C1%2C8%29%29

There are three operations that you can perform:
1. Swap the position of any two rows
2. Multiply any row by any scalar quantity
3. Replace any row with the sum of that row and another row.

The goal is to manipulate the matrix until you have the following situation:
%28matrix%282%2C3%2C1%2C0%2Ca%5B1%5D%2C0%2C1%2Ca%5B2%5D%29%29

Start by multiplying Row 1 by 1%2F2
%28matrix%282%2C3%2C1%2C-1%2F2%2C7%2F2%2C3%2C1%2C8%29%29

Next, multiply row 1 by -3, add the result to row 2 and then replace row 2 with that result:
Row 1 times -3: matrix%281%2C3%2C-3%2C3%2F2%2C-21%2F2%29
Result plus Row 2: matrix%281%2C3%2C0%2C5%2F2%2C-5%2F2%29 because (-21%2F2%2B16%2F2=-5%2F2)
Resulting matrix: %28matrix%282%2C3%2C1%2C-1%2F2%2C7%2F2%2C0%2C5%2F2%2C-5%2F2%29%29

Multiply Row 2 by 2%2F5
%28matrix%282%2C3%2C1%2C-1%2F2%2C7%2F2%2C0%2C1%2C-1%29%29

Multiply Row 2 by 1%2F2, add the result to row 1, and replace row 1 with the result:
Row 2 times 1%2F2: matrix%281%2C3%2C0%2C1%2F2%2C-1%2F2%29
Result plus Row 1: matrix%281%2C3%2C1%2C0%2C3%29
Resulting matrix: %28matrix%282%2C3%2C1%2C0%2C3%2C0%2C1%2C-1%29%29

Hence: x=3 and y=-1

Check:
2x-y-7=0
2%283%29-%28-1%29-7=6%2B1-7=0 True

3x%2By=8
3%283%29%2B%28-1%29=9-1=8 Also True, answer checks.