SOLUTION: Perform an operation on the given system that eliminates the indicated variable and solve for the unknown variables. x-4y+z=3 y-3z=10 3y-8z=24

Question 307509: Perform an operation on the given system that eliminates the indicated variable and solve for the unknown variables.
x-4y+z=3
y-3z=10
3y-8z=24
Answer by rapaljer(4671) (Show Source): You can put this solution on YOUR website!
Multiply the second equation by -3 and add to the third equation.

-3y+9z=-30
3y-8z=24
z=-6

Now, substitute z=-6 into the second equation:
y-3x=10
y-3*-6=10
y+18=10
y=-8

Finally, substitute both z and y into the first equation:
x-4y+z=3
x-4(-8)+-6=3
x+32-6=3
x=3+6-32=-23

I used a program in my TI84 called "POLYSIMULT" to check this answer. If you are interested in this, send me an Email at rapaljer@seminolestate.edu.

Dr. Robert J. Rapalje, Retired

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