SOLUTION: Solve the system of equations: -3x + y - z = -10 -4x + 2y + 3z = -1 2x + 3y - 2z = -5

Algebra ->  Equations -> SOLUTION: Solve the system of equations: -3x + y - z = -10 -4x + 2y + 3z = -1 2x + 3y - 2z = -5       Log On


   

Question 423897: Solve the system of equations:
-3x + y - z = -10
-4x + 2y + 3z = -1
2x + 3y - 2z = -5
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
From the 1st equation, we get z = -3x + y + 10.
Into the 2nd equation: -4x + 2y + 3(-3x + y + 10) = -1,
<==> -4x + 2y - 9x+ 3y + 30 = -1
<==> -13x + 5y = -31
Into the 3rd equation: 2x + 3y - 2(-3x + y + 10) = -5
<==> 2x + 3y + 6x - 2y - 20 = -5
<==> 8x + y = 15 ==> y = 15 - 8x
==> -13x + 5(15 - 8x) = -31
==> -13x + 75 - 40x = -31
-53x = -106
==> x = 2.
==> y = 15 - 8*2 = 15 - 16 = -1
==> z = -3*2 + (-1) + 10 = -6 - 1 + 10 = 3