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!

Tutors, sign in to answer this question.

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.

Already have an account? Log in

By signing up, I agree to Wyzant’s terms of use and privacy policy.

Or

To present the tutors that are the best fit for you, we’ll need your ZIP code.

Your Facebook email address is associated with a Wyzant tutor account. Please use a different email address to create a new student account.

Good news! It looks like you already have an account registered with the email address **you provided**.

It looks like this is your first time here. Welcome!

To present the tutors that are the best fit for you, we’ll need your ZIP code.

Please try again, our system had a problem processing your request.