# SOLUTION: Use elimination method to solve the system. -4x+4y-2z=-8 -3x-y+4z=0 2x-2y+3z=-4

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 Question 160700: Use elimination method to solve the system. -4x+4y-2z=-8 -3x-y+4z=0 2x-2y+3z=-4Answer by ankor@dixie-net.com(15652)   (Show Source): You can put this solution on YOUR website!-4x + 4y - 2z =-8 -3x - y + 4z = 0 +2x- 2y + 3z =-4 : The coefficients of the 1st and 3rd equations, will help us alot: : Multiply the 3rd equation by 2, and add to the 1st equation -4x + 4y - 2z = -8 +4x - 4y + 6z = -8 ---------------------adding eliminates x and y, find z 0x + 0y + 4z = -16 z = z = -4 : Substitute -4 for z in the 2nd equation -3x - y + 4(-4) = 0 -3x - y - 16 = 0 -3x - y = 16 : Substitute -4 for z in the 3rd equation: +2x - 2y + 3(-4) = -4 +2x - 2y - 12 = -4 +2x - 2y = -4 + 12 +2x - 2y = +8 : Multiply -3x - y = 16 by -2 and add to the above equaiton +6x + 2y = -32 +2x - 2y = 8 ---------------- addition eliminate y 8x = -24 x = x = -3 : Find y using the 2nd equation, substitute for x & z -3(-3) - y + 4(-4) = 0 +9 - y - 16 = 0 -y -7 = 0 -y = +7 y = -7 : Solutions: x=-3, y=-7; z=-4 : : Check solutions in the 3rd equation: +2x- 2y + 3z =-4 2(-3) - 2(-7) + 3(-4) = -4 -6 + 14 - 12 = -4 -18 + 14 = -4