Math

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mashra mashra
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Math



Please solve, gracias.  
Proof Proof
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Re: Math

2x + y - z = -1
x - 2y + 2z = 12
2x + 2y + z = -6


2x + y - z = -1
2x + 2y + z = -6  
--------------------
-y - 2z = 5   ← subtracted first and third equations


2x + y - z = -1    ----->  2x + y - z = -1   ← first equation stays the same
x - 2y + 2z = 12  ---->  -2x + 4y - 4z = -24   ← multiplied second equation by -2
                                   ----------------------
                                          5y - 5z = -25   ← added the two equations

-y - 2z = 5  ------>  -5y -10z = 25   ← multiplied first new equation by 5
5y - 5z = -25  ---->  5y - 5z = -25  ← second new equation stays the same
                              ----------------
                                    -15z = 0   ← added the two new equations
                                      z = 0   ← divided each side by -15

5y - 5z = -25   ← equation with x and z taken from above
5y - 5(0) = -25   ← substituted 0 for z
5y  = -25   ← multiplied
y = -5   ← divided each side by 5

x - 2y + 2z = 12  ← equation taken from above
x - 2(-5) + 2(0) = 12   ← substituted 0 for z and -5 for y
x + 10 = 12   ← multiplied
x = 2   ← subtracted 10 from each side

x = 2, y = -5, and z = 0

- Proof