Question 153430
 2x+6y+8z =5
-2x+9y-12z=-1
 4x+6y-4z =3
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+2...+6...+8....+5
-2...+9...-12...-1
+4...+6...-4....+3
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Add 1st to 2nd to get: 
+2...+6...+8....+5
+0...+15..-4....+4
+4...+6...-4....+3
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Add -2 times the 1st to the 3rd to get:
+2...+6...+8....+5
+0...+15..-4....+4
+0...-6..-20....-7
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Add 3rd to 1st to get:
+2...+0...-12...-2
+0...+15..-4....+4
+0...-6..-20....-7
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Divide thru equation 3 by -6:
+2...+0...-12...-2
+0...+15..-4....+4
+0...+1..+10/3..+7/6
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Add -15 time 3rd to the 2nd to get:
+2...+0...-12...-2
+0...+0...-54...-13.5
+0...+1..+10/3..-7/6
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Solve the 2nd equation for z:
-54z = -13.5
z = 0.25 or 1/4
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Substitute z = 1/4 into the 3rd equation to solve for "y":
y +(10/3)(1/4) = -7/6
y + (5/6) = -7/6
y = -2
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Substitute z = 1/4 into the 1st equation to solve for "x"
2x -12*(1/4) = -2
2x - 3 = -2
2x = 1
x = 1/2
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Final solution:
x = 1/2
y = -2
z = 1/4
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Cheers,
Stan H.