Question 12428: please help me solve this problem.
Solve the system using any algebraic method
x + y + 2z =5
x + 2y + z = 8
2x + 3y - z = 1
Thanks for helping me solve this problem.
KAt
Answer by AnlytcPhil(1806)   (Show Source):
You can put this solution on YOUR website!
`x +` y + 2z = 5
`x + 2y +` z = 8
2x + 3y -` z = 1
`
One way is to eliminate the three lower left terms,
the ones I have colored red:
`
`x +` y + 2z = 5
`x + 2y +` z = 8
2x + 3y -` z = 1
`
Instead of solving yours, I'll solve one just like it, OK?
Then you can use it as a model to solve yours.
`
`x - 3y + 4z =` 45
3x + 2y - 5z = -21
4x + 5y - 3z = -32
`
`x - 3y + 4z = `45
3x + 2y - 5z = -21
4x + 5y - 3z = -32
`
To get rid of the 3x, multiply the top equation by -3
and add it to 1 times the middle equation, but restore the
top equation:
`
-3[ x - 3y + 4z =` 45]
`1[3x + 2y - 5z = -21]
` `4x + 5y - 3z = -32
`
`x - 3y +` 4z = ` 45
` ` 11y - 17z = -156
4x + 5y -` 3z =` -32
`
To get rid of the 4x, multiply the top equation by -4
and add it to 1 times the bottom equation, but again
restore the top equation:
`
-4[ x - 3y +` 4z = ` 45]
` ` ` `11y - 17z = -156
`1[4x + 5y - `3z = `-32]
`
x - 3y + `4z = ` 45
` `11y - 17z = -156
` `17y - 19z = -212
`
To get rid of the last one, 17y, multiply the middle equation by -17 and add it to 11 times the bottom equation, but
restore the middle equation:
`
` ` x - 3y + 4z = ` 45
-17[ ` 11y - 17z = -156
`11[ ` 17y - 19z = -212
`
x - 3y + `4z = ` 45
`` 11y - 17z = -156
` ` ` ` `80z = 320
`
Now that those three bottom left terms have been
eliminated, solve the bottom equation:
`
` ` ` ` `80z = 320
` ` ` ` ` `z = 4
`
Substitute z=4 into the middle equation and solve
for y
`
`11y - 17(4) = -156
` ` 11y - 68 = -156
` ` ` ` `11y = -88
` ` ` ` ` `y = -8
`
Fimally substitute z=4 and y=-8 into the top equation and solve for x:
`
x - 3(-8) + 4(4) = 45
` ` `x + 24 + 16 = 45
` ` ` ` ` x + 40 = 45
` ` ` ` ` ` ` `x = 5
`
So the solution is (x, y, z) = (5, -8, 4)
`
Now use this as a model to solve yours by. The solution is
`
(x, y, z) = (-7, 6, 3)
Edwin
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