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Three equations/three unknowns

I need to solve the following system of three equations and describe the methods used could you please assist and explain it in detail so I can apply it to the other problems.
eq1: X + Y + Z = 6
eq2: 2X - Y + 3Z = 8
eq3: 3X - 2Y - Z = -17

Solution Summary

This provides an example of solving a system of three equations.