Question 1109682: Solve the following system of 3 equations. Be sure to indicate which is your working equation and which is your focus variable. 2x+4y-z=1 and 3x+3y+4z=1 and -5x-8y+6z=5.
Answer by rothauserc(4718)   (Show Source):
You can put this solution on YOUR website! (1) 2x +4y -z = 1
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(2) 3x +3y +4z = 1
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(3) -5x -8y +6z = 5
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multiply equation 1 by 6 and add it to equation 3
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(4) 7x +16y = 11
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multiply equation 1 by 4 and add it to equation 2
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(5) 11x +19y = 5
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equations 4 and 5 are two equations in two unknowns
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solve equation 4 for x
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x = (11 -16y)/7
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substitute for x in equation 5
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11*((11 -16y)/7) +19y = 5
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((121 -176y)/7) +19y = 5
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multiply both sides of = by 7
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121 -176y +133y = 35
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-43y = -86
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y = 2
x = (11 -16(2))/7 = -3
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use equation 1 to get the value for z
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2(-3) +4(2) -z = 1
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-6 +8 -z = 1
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-z = -1
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z = 1
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x = -3, y = 2, z = 1
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check answers by substituting in equations 1, 2 and 3
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(1) 2(-3) +4(2) -1 = 1
-6 +8 -1 = 1
1 = 1
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(2) 3(-3) +3(2) +4(1) = 1
-9 +6 +4 = 1
1 = 1
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(3) -5(-3) -8(2) +6(1) = 5
15 -16 +6 = 5
5 = 5
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the answer checks
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