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Solve the system
x - y + z = 0 (1)
x + y + z = -2 (2)
x + y - z = 8 (3)
This system is special. It is possible to solve it using the mental math only.
Distract first equation from the second ((1) from (2)). You will get
2y = -2. Hence, y = -1.
Next, distract equation (3) from (2). You will get
2z = -10. Hence, z = -5.
Finally, substitute the found values y= -1 and z= -5 into the first equation. You will get
x - (-1) + (-5) = 0, or x = 5 - 1 = 4.
Answer. The solution is x= 4, y= -1 and z= -5.
