SOLUTION: Could you please take the time to help me solve this problem: Solve the following system of three linear equations: x – 2y = 4 and 2 x – 3 y + 2 z = – 2 and 4 x – 7 y + 2 z = 6.

Algebra ->  Algebra  -> Coordinate Systems and Linear Equations -> SOLUTION: Could you please take the time to help me solve this problem: Solve the following system of three linear equations: x – 2y = 4 and 2 x – 3 y + 2 z = – 2 and 4 x – 7 y + 2 z = 6.       Log On

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Question 102281: Could you please take the time to help me solve this problem: Solve the following system of three linear equations: x – 2y = 4 and 2 x – 3 y + 2 z =
– 2 and 4 x – 7 y + 2 z = 6. Noting that each equation represents a plane, interpret your result.
Thank you, for taking the time to help me
Answer by stanbon(48546) About Me  (Show Source):
You can put this solution on YOUR website!
x – 2y 0z = 4
2 x – 3 y + 2 z = – 2
4 x – 7 y + 2 z = 6
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x = 2y+4
Substitute to get:
2(2y+4)-3y+2z = -1
4(2y+4)-7y+2z = 6
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Simplify:
x = 2y+4
y + 2z = 9
y + 2z = -2
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The last two equations indicate the system is inconsistent.
Two of the equations represent parallel planes.
There is no intersection of the three planes represented
by the original three equations.
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Cheers,
Stan H.