Question 125122: the following system is dependent. Solve system showing the solution in terms of z
X - Y + Z = 3
X - 2Y - Z = 5
Answer by ilana(307)   (Show Source):
You can put this solution on YOUR website! I have actually never seen a question like this, but what it is asking you to do is solve for X and Y, and pretend Z is a number. So your solutions for X and Y will have Z in them.
First, I would combine the 2 equations by subtracting the second from the first. That way X will go away and I can solve for Y. So (X-Y+Z=3)-(X-2Y-Z=5) =(X-Y+Z-Z+2Y+Z=3-5).
So Y+2Z=-2, so Y=-2-2Z. Now plug that back into the first equation to solve for X.
X-Y+Z=3 becomes X-(-2-2Z)+Z=3, so X+2+2Z+Z=3, so X+2+3Z=3, so X=1-3Z.
So X=1-3Z, Y=-2-2Z is the solution.
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