SOLUTION: this question is from a wksht...can you still help me? 2x-y-z=2 -x+3y+z=-1 2x-4y-3z=-5 i started the problem and for y i got -5/7 and -32/7 for z...i dont think that is right

Algebra ->  College  -> Linear Algebra -> SOLUTION: this question is from a wksht...can you still help me? 2x-y-z=2 -x+3y+z=-1 2x-4y-3z=-5 i started the problem and for y i got -5/7 and -32/7 for z...i dont think that is right      Log On


   

Question 121843: this question is from a wksht...can you still help me?
2x-y-z=2
-x+3y+z=-1
2x-4y-3z=-5
i started the problem and for y i got -5/7 and -32/7 for z...i dont think that is right
Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!
I would have liked to see the work you did to get to the answers you gave. You are correct in thinking your results are incorrect. I proved it to myself by substituting your values into the first equation, solving for x, and then substituting all three values into the second equation. That exercise resulted in a false statement something along the lines of -%2869%2F14%29=-1.

So, let's begin anew.

1. 2x-y-z=2
2. -x%2B3y%2Bz=-1
3. 2x-4y-3z=-5

Add the equation 1 to the equation 2, resulting in:

4. x%2B2y%2B0z=1, and set this aside for later

Multiply equation 2 by 3, resulting in:

5. -3x%2B9y%2B3z=-3

Add eq 5 to eq 3, resulting in:

6. -x%2B5y%2B0z=-8

Add eq 4 to eq 6, resulting in:

0x%2B7y=-7
y=-1

Substitute -1 for y in eq 4:

x%2B2%28-1%29=1
x-2=1
x=3

Substitute 3 for x and -1 for y in equation 1:

2%283%29-%28-1%29-z=2
6%2B1-z=2
7-z=2
z=5

And the solution set is the ordered triple (3,-1,5).

To check the answer, substitute the x, y, and z coordinates of the solution ordered triple into each of the original equations. If you get a true statement each time, you have verified the answer. I'll let you do the arithmetic.