SOLUTION: 2x + 4y + 4z = 16 2x - y + 3z = 9 3x + 4y

SOLUTION: 2x + 4y + 4z = 16 2x - y + 3z = 9 3x + 4y - z = 8

Question 475310: 2x + 4y + 4z = 16
2x - y + 3z = 9
3x + 4y - z = 8
Answer by ccs2011(207) (Show Source): You can put this solution on YOUR website!
I think the best way to do these is using the elimination method.
Eliminate a variable to break it down into a system of 2 equations, then use elimination again to break it down to a single equation. Solve for that variable and then use substitution to find the 2nd variable in the system of 2 equations. Then substitute both those values into one of the original equations to find 3rd variable.
Let me label each equation: A,B,C for reference
A:
B:
C:
Notice A and C both have a 4y, therefore it will be easiest to eliminate variable y. Multiply C by -1. Add A and C. Call the resulting equation D.
D:
We still need another equation with x and z. To eliminate y again. Multiply B by 4. Add A and B. Call the resulting equation E.
E:
Now eliminate x. Multiply D by 10. Add D and E.

Solve for z. Divide by 66 on both sides.

Substitute z=2 into D.

Solve for x.

Subtract 10 on both sides

Flip signs

Substitute x=2, z=2 into B.

Solve for y

Subtract 10 on both sides

Flip signs

Verify solution by substituting into other equations A and C.

True...it works.

True..it works.
Solution is x = 2, y = 1, z = 2

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