Solve the following system of equations.

Question

anonymous · Answer

2x + 2y + z = 10 
3x − y + 3z = 10 
2x + 3y − 2z = 6

 (2, 2, 2)

 (−2, 2, 2)

 (2, −2, 2)

 (2, 2, −2)

hero · Answer

Is there a particular method that you're expected to use for this?

anonymous · Answer

im not sure. maybe elimination?

anonymous · Answer

it didn't say

hero · Answer

I guess what I meant to ask is, are you familiar with matrices?

anonymous · Answer

im not

hero · Answer

If not, then that's okay too. As far as algebraic methods of elimination, there are two approaches. One involves the triangulation method. The other involves setting up two systems of equations.

anonymous · Answer

Okay, cool!

hero · Answer

With the triangulation method you put the system in the form 

ax + by + cz = d
        ey + fz = g
                 z = j

anonymous · Answer

can we do elimination?

hero · Answer

The triangulation method is one method of elimination.

hero · Answer

I'm just trying to figure out what you're familiar with.

hero · Answer

Actually, one quicker method might be to simply plug in the answer choices.

anonymous · Answer

okay:)

anonymous · Answer

can you help me?

hero · Answer

Let me know how it goes.

anonymous · Answer

okay!

hero · Answer

Wait, are you planning to insert the answer choices?

hero · Answer

Like for example, try pluggin in the first choice (2, 2, 2)

anonymous · Answer

okay yeah i did that

hero · Answer

Believe it or not, you can actually do this process in your head.

hero · Answer

but let me show you how: 

2(2) + 2(2) + 2 = 10 
3(2) − (2) + 3(2) = 10 
2(2) + 3(2) − 2(2) = 6

anonymous · Answer

yeah i did that! :)

anonymous · Answer

i get it now, haha thank you

hero · Answer

Evaluate each equation. All you need is one equation to be false for the choice to be incorrect.

hero · Answer

If that choice doesn't work, try (-2, 2, 2)

anonymous · Answer

okay, so its not A

hero · Answer

Great :) 

Keep going until you find the right now.