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My problem is to graph a system of inequalities (which ive done) and introduce slack variables to convert the system of inequalities to a system of equations. So I am building my table and all is easy until I get to the point where S1 and S2 are both zeros or S1 and S3 are zeroes or S2 and S3 are both zeros???? Below is the equation but how am i supposed to solve besides continuaslly guessing and checking (which is how I did 2 of them)

3* x1 + x2 + S1 =105
x1 + x2 + S2 =37
x1 + 3* x2 + S3 =48

So when S1 & S2 were 0's i figured it out x1=34, x2=3 & S3=5 Then when S1 & S3 were both 0's I figured that out which took forever at 33.375,4.875 & -1.2. But i was just guessing and checking. Can someone please help me understand the correct way to solve these?

Thanks in advance.

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