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$$\begin{array}{rcrcrcr} x & - & 2y & + & 3z & = & 7 \\\ 2x & + & y & + & z & = & 4 \\\ -3 x & + & 2y &- &2z & = & -10 \end{array}$$

I have no idea how to do this and my math book is just telling me to do it, and explains nothing. I have a problem containing 3 equations with 3 variables. What do I do? I tried to solve for x and y and then find z but that didn't work and I got the wrong answer. What do I do? My book tells me to "Multiply each side of equation by -1 and add the result to equation 2, also add equations 2 and 3" I have no idea what this means or why they do it, it is never explained in this book anywhere and they seem like completely arbirtrary number not dependent upon anything, like the author is doing it for fun.

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    It may be helpful if you include the actual system of equations you are working with.2011-04-16
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    Maybe it would be a good idea to post the problem you're talking about and show what you did, because like that one can't do much more than point you to [Wikipedia](http://en.wikipedia.org/wiki/Gaussian_elimination). (ah, @yunone you beat me by 17 seconds!)2011-04-16
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    Do you know how to solve 2 equations with 2 variables?2011-04-16
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    Yes, I know how to do 2 variables, but with 3 the book is telling me to multiply by the coefficients on one variable to solve for the others or something very strange, and then add them. I have no idea, it doesn't explain at all. x-2y+3z = 7 2x+y+z = 4 -3x+2y-2z = -10 I got z= -1 but that isn't right.2011-04-16
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    @Theo, whoops, didn't mean to snipe your comment there!2011-04-16
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    @Adam, have you tried to express one of the variables in terms of the other two using one equation (for instance $z$ in terms of $x$ and $y$) and then substitute this into the remaining equations. This way, you are left with a system with only two variables.2011-04-16
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    Why is my book telling me to multiply the first equation by a number related to the coefficient, do the same with the second, add them together and then attempt to solve the third?2011-04-16
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    @Adam: The point of these operations is to simplify the equations. If $x+y=1$ and $x-y=0$ say, then by adding the two equations, you see that $2x=1$, which immediately gives you the solution for $x$. Adding up equations is perfectly OK, if the two sides are equal, adding them up should still result in an equality.2011-04-16
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    What two sides have to be equal and how do you do it?2011-04-16
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    Are you describing different methods? I am attempting to do subsitution as I was told it was the easiest and best way to do it, I tried the other way and did not like it. I know subsititution, is this still it?2011-04-16

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