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All you are doing is stripping the variables away to get the coefficients. That's all you have to do, to solve you can use a TI-83 calculator.
So the matrix would be
7 4 5 62
5 3 2 47
3 7 8 63
Its easy you just take the coefficients ( numbers) and throw the letters away.
Then get your calculator and press 2nd---> MATRIX
Select a grid and set up the rows and columns in this case it is 3X4.
Select it again and it will open up a window where you can enter the coefficients.
Then exit to home screen, and press 2nd Matrix again, then scroll over to the right and select MATH, scroll down until you find rref, hit that and then go back into the Matrix menu and select your 3X4 grid, hit a parentheses key to make the 3X4 grid enclosed then press enter.
It will give you the solutions in a 3X4 grid it should contain a bunch of 1's and 0's.