# Math

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## Math

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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