You can put this solution on YOUR website! -4x + 4y - 2z =-8
-3x - y + 4z = 0
+2x- 2y + 3z =-4
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The coefficients of the 1st and 3rd equations, will help us alot:
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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
:
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Check solutions in the 3rd equation:
+2x- 2y + 3z =-4
2(-3) - 2(-7) + 3(-4) = -4
-6 + 14 - 12 = -4
-18 + 14 = -4
