3x+y+z=13

2x+2y-3z+3

3x+y-z=7

A) (2,-4,11)

B) (3,4,0)

C) (2,4,3)

D)(6,-3,4)

3x+y+z=13

2x+2y-3z+3

3x+y-z=7

A) (2,-4,11)

B) (3,4,0)

C) (2,4,3)

D)(6,-3,4)

Tutors, please sign in to answer this question.

Wallingford, CT

One way to solve a system of three variables is to create a system of two variables by using combinations of the three equations in such a way to eliminate the third variable. It is important that you use all three equations to do this. For example I will multiply the first equation by 3 and add it to the second equation:

3(3x + y +z = 13) = 9x + 3y + 3z = 39

9x + 3y + 3z = 39

+ 2x + 2y -3z = 3

11x + 5y + 0z = 42

To get a second equation, I will multiply the third equation by -3 and add it to the second equation:

-3(3x+y-z=7) = -9x - 3y + 3z = -21

-9x - 3y + 3z = -21

+ 2x + 2y - 3z = 3

-7x - y + 0z = -18

Now we have a system of two equations:

11x + 5y = 42

-7x - y = -18

Use either the substitution method or elimination method to solve this system for x and y. Once you have x and y, plug those in to any of the original equations to solve for z. Plug in this (x,y,z) coordinate into all three of the equations, to make sure that it satisfies each constraint.

Alex C.

Harvard/MIT Finance and Statistics Tutor

Fort Lee, NJ

5.0
(281 ratings)

Lorraine S.

Lorraine's Literacy and Learning for Life

Staten Island, NY

4.9
(489 ratings)

Daniel B.

Experienced Harvard Grad For SAT Prep and K-6 Reading

Teaneck, NJ

5.0
(81 ratings)

- Math Help 5187
- Algebra 4899
- Math Word Problem 4241
- Calculus 2162
- Word Problem 4940
- Algebra 2 3294
- Algebra 1 3929
- Math Problem 970
- Math Help For College 1357
- Math Equations 936