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.

Avital S.

Patient tutor, for all ages, helps when your learning is blocked

Westwood, NJ

5.0
(504 ratings)

Wesley L.

Premier MIT Math Tutor and SHSAT/SAT/ACT Specialist

New York, NY

5.0
(211 ratings)

Sean B.

Premier NYC Math tutor - young, passionate and talented

New York, NY

5.0
(24 ratings)

- Math Help 4189
- Algebra 4064
- Calculus 1769
- Math Word Problem 3083
- Algebra 2 2863
- Word Problem 4040
- Algebra 1 3249
- Math Equations 892
- Math Problem 795
- Math Help For College 1212