Solve the system:

2x-3y-z=5

-2x+3y+z=-5

8x-12y-4z+20

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!

Solve the system:

2x-3y-z=5

-2x+3y+z=-5

8x-12y-4z+20

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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Blacksburg, VA

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 :)

New Wilmington, PA

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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