System Of Equations With Products Of Variables
Date: 10/29/2003 at 18:17:24 From: Katie Siemens Subject: solving systems of equations I'm trying to solve the following system of equations for (x,y,z): xy + zx = -1 xy + yz = -9 yz + zx = -4 I know that I need to solve for a variable and substitute it in and solve but I can never get rid of the varriables to get actual answers. My answers just keep getting more and more complex! For example, I can figure out that: x = -1/(y + z) y = -9/(x + z) z = -4/(y + x) but it doesn't seem to get me anywhere. Can you help?
Date: 10/29/2003 at 23:39:39 From: Doctor Ian Subject: Re: solving systems of equations Hi Katie, In this case, elimination may work better than substitution. Suppose we subtract the second equation from the first: xy + zx = -1 - (xy + yz = -9) ----------------------- zx - yz = -1 - -9 zx - yz = 8 Now, what if we add that new equation to the third original equation? zx - yz = 8 + zx + yz = -4 ---------------- 2zx = 8 + -4 2zx = 4 zx = 2 Okay, that's a start! Now you can use substitution to go back and find out what xy and yz are. Then you'll have a system that looks like this: xy = ? yz = ? zx = 2 Can you take it from there? - Doctor Ian, The Math Forum http://mathforum.org/dr.math/
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