SOLUTION: Solve systems of three variables. linear eqations 2x+2y+z=1 -x+y+2z=3 x+2y+4z=0

Question 824681: Solve systems of three variables. linear eqations
2x+2y+z=1
-x+y+2z=3
x+2y+4z=0
Answer by TimothyLamb(4379) (Show Source): You can put this solution on YOUR website!
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2x+2y+z=1
-x+y+2z=3
x+2y+4z=0
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copy and paste the above standard form linear equations in to this (matrix method) solver:
https://sooeet.com/math/system-of-linear-equations-solver.php
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answer:
x= -2
y= 3
z= -1
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NOTE TO STUDENT:
now solve by elimination:
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-x+y+2z=3
x+2y+4z=0
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add this sub-system and call it A:
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3y+6z=3
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2x+2y+z=1
2(-x+y+2z=3)
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add this sub-system and call it B:
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4y+5z=7
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the A and B sub-system:
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3y+6z=3
4y+5z=7
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add the A and B sub-system:
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-4(3y+6z=3)
3(4y+5z=7)
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-9z=9
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z = -1
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substitute z in B:
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4y+5(-1)=7
4y=12
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y = 3
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substitute y and z in any of the original equations:
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x+2(3)+4(-1)=0
x+6-4=0
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x = -2
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answer by elimination:
x= -2
y= 3
z= -1
NOTE: the matrix method (used by the above solver), and the elimination method agree
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Solve and graph linear equations:
https://sooeet.com/math/linear-equation-solver.php
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Solve quadratic equations, quadratic formula:
https://sooeet.com/math/quadratic-formula-solver.php
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Solve systems of linear equations up to 6-equations 6-variables:
https://sooeet.com/math/system-of-linear-equations-solver.php
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