Question

Solve the following system of equations.

3x – 2y + z = –6
x – 3y + z = –3
2x + y – 2z = –7

Answer 1

The options:
(–3, –6, –7)
(1, –3, 3)
(–2, 1, 2)
(1, 5, 1)

Answer 2

You should try to set up for eliminating a variable in two cases, to get a system of 2-variable equations.
3x - 2y + z = -6
2x + y - 2z = -7 <-- Eliminate the 'z's

x - 3y + z = -3
2x + y - 2z = -7 <-- Eliminate the 'z's

Answer 3

In this case, we can multiply the first equation (in both cases) by 2 to set up for the elimination.

Answer 4

you can solve it by a long process but since you have the options, a bit of trick will do.
Substitute the points in the given equations one by one and see which one satisfies all equations.
Here, third option satisfies all equations! so, that's it.

Answer 5

Thank you both! Much appreciated. :)

Answer 6

I recommend @AccessDenied's process for a better understanding of mathematics!

Answer 7

The process just gets tedious since its just eliminating variables. Once you have the 2-variable system, you just eliminate another variable in that system to get 1-variable, solve for it, and then you just substitute into a 2-variable equation for the next, and then a 3-variable for the third.