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Question 98227: My assignment is to solve the system of equations: 3x + 4y+ z = 7, 2y + z = 3, -5x + 3y + 8z = -31
But it seems unsolveable to me. I see no way to eliminate any variables.
What am I missing?
Answer by kev82(151)   (Show Source):
You can put this solution on YOUR website! Hi,
I don't know how you've been taught to do these, but by the sounds of it, it's by subtraction. I'm going to try and eliminate z by using the second equation. Both the first and second equations have a single z in, so if I subtract them, I will cancel the z term.
(3x+4y+z) - (2y+z) = 7 - 3
3x+2y = 4
The third equation has 8 zeds in it. So we need to subtract the second equation 8 times (or subtract 8* the second equation) from the third equatuation to get rid of all the zeds.
(-5x+3y+8z) - 8(2y+z) = -31 - 8*3
-5x-13y = -55
5x+13y = 55
So there I have eliminated z, can you now either eliminate x or y from these two equations to get the answer?
Kev
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