Question 709505: *Solving systems of Linear Equations in Three Variables by Elimination*
does anyone know how to solve x,y,z equations for x and explain?!
2x + y + z = 0
3x - y + z = 3
7x - 5y - 3z = 15
thanks!
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! solve x,y,z equations for x and explain?!
2x + y + z = 0
3x - y + z = 3
7x - 5y - 3z = 15
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Setting up:
Subtract 1st row from 2nd and make the difference the 1st row:
x - 2y + 0 = 3
2x + y + z = 0
7x - 5y - 3z = 15
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Subtract 2*1st row from 2nd row
Subtract 7*1st row from 3rd row
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x - 2y + 0 = 3
0 + 5y + z = -6
0 + 9y -3z = -6
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Solve equations 2 and 3 for y and z:
5y + z = -6
3y - z = -2
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Add and solve for "y":
8y = -8
y = -1
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Solve for "z" using 3y-z = -2
3*-1 -z = -2
z = -1
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Solve for "x" using
2x + y + z = 0
2x + -1 + -1 = 0
x = 1
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Solution:
x = 1
y = -1
z = -1
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Cheers,
Stan H.
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