Question 1097959: Solve the system using substitution.
3x + 4y − z = 14
x − 5y + 2z = 26
5x + y − 2z = 40
The solution to the system of three linear equations is the ordered triple____.
Answer by Alan3354(69443)   (Show Source):
You can put this solution on YOUR website! Solve the system using substitution.
3x + 4y - z = 14 times 2 --> 6x + 8y - 2z = 28
x - 5y + 2z = 26
5x + y - 2z = 40
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6x + 8y - 2z = 28 --> 2z = 6x + 8y - 28
x - 5y + 2z = 26
5x + y - 2z = 40
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Sub for 2z in Eqns 2 & 3
x - 5y + 2z = 26
x - 5y + 6x + 8y - 28 = 26
7x + 3y = 54 --- Eqn A
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5x + y - 2z = 40
5x + y - (6x + 8y - 28) = 40
-x - 7y = 12 --- Eqn B
-7x - 49y = 84 --- Eqn B times 7
7x - y = 54 --- Eqn A
-------------------------------- Add
-50y = 138
y = -69/25
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Sub for y in Eqn A or B, find x
Sub for x & y in any equation, find z
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Don't solve for x, y or z and deal with fractions.
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check the work carefully.
It's easy to make a mistake, and it's late and I'm tired.
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