SOLUTION: Solve the system. x-y+z=0 x+y+z=-2 x+y-z=8

Algebra.Com
Question 1004970: Solve the system.
x-y+z=0
x+y+z=-2
x+y-z=8
Found 2 solutions by Alan3354, ikleyn:
Answer by Alan3354(69443)   (Show Source): You can put this solution on YOUR website!
I just did one like that.
Same problem, different numbers.
Look it up.
Answer by ikleyn(52781)   (Show Source): You can put this solution on YOUR website!
.
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.


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