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Expert: - 11/18/2008


Question
Solving Systems of Equations using Elimination
(with 3 variables)
Here is the problem:

-5x-z=2
x+4y-2z=1
2x-4y-z=-13

I know how to solve if all three equations have all variables. I'm having a problem with this one because the first equation is missing the y variable and I don't know what to do.

Any help is appreciated.  Thanks.

Answer
Make the first equation -5x + 0y -z = 2, so now we have a y in the first equation.

Either that or add the second and third equation to give another equation with x and z alone.  Take this with the first equation and you have two equations with two unknowns (an easier problem).  Once x and z have been found, put them back in the original equations and y can be gotten.

Use either the second or third equation to find y.  Both could be used to make sure that it was done correctly, for both should give the same value of y.

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