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Find the solution to the system of equations 3x plus y plus z equals 6 3x - y plus 2z equals 9 y plus z equals 3?
3x + y + z = 6
3x - y + 2z = 9
y + z = 3
y + z = 3
y = 3 - z (substitute 3 - z for y into the first equation of the system)
3x + y + z = 6
3x + (3 - z) + z = 6
3x + 3 = 6
3x = 3
x = 1 (substitute 3 - z for y and 1 for x into the second equation of the system)
3x - y + 2z = 9
3(1) - (3 - z) + 2z = 9
3 - 3 + z + 2z = 9
3z = 9
z = 3 (which yields y = 0)
y = 3 - z = 3 - 3 = 0
So that solution of the system of the equations is x = 1, y = 0, and z = 3.
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