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Solving Linear Equations in Three Variables

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2 Answers

Hey Courtnee -- its often helpful add/subtract expressions, sometimes doubling/halving them ...
 
here we don't have 3 different expressions: (2) is the negative of (1), (3) is (1) rescaled by 4 :)
We have one equation with three variables:
 
2x-3y-z=5
 
(Your other two equations are just multiples of this equation.)
 
You can solve it for any one variable, eg.
 
z=2x-3y-5
 
which has infinitely many solutions, namely all points of the form
 
(x,y,2x-3y-5), where x and y are any real numbers.
 
Geometrically, the solution set corresponds to a plane in 3-space.

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