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Solving Linear Equations in Three Variables

Solve the system:
How I understand it is the 2x+-2x along with the -3y+3y and -z+z can cancel each other out.  I am having trouble figuring out what to do next.  Any help will be appreciated!
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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:
(Your other two equations are just multiples of this equation.)
You can solve it for any one variable, eg.
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.