SOLUTION: Use Gaussian elimination to find the complete solution to the following system of equations, or show that none exists. x-y+z=5 2x+3y-3z=0

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Question 814129: Use Gaussian elimination to find the complete solution to the following system of equations, or show that none exists.
x-y+z=5
2x+3y-3z=0
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
 1  -1    1   5
 2   3   -3   0
Add -2 times the first row to the second row:
 1  -1    1    5
 0   5   -5  -10
Multiply the second row by 1/5:
 1  -1    1    5
 0   1   -1   -2
Add the second row to the first:
 1   0    0    3
 0   1   -1   -2
This is as far as we can go. It translates into:
x = 3
y - z = -2 or y = z - 2
So there are an infinite number of solutions. The x must be 3 but the y and z values can be any numbers which fit either y - z = -2 or y = z - 2.One way to express the solution is: (3, z-2, z)