Solve the following system of equations:

x + 3y - z = 2
x - 2y + 3z = 7
x + 2y - 5z = -21

Question

Solve the following system of equations:

x + 3y - z = 2 
x - 2y + 3z = 7
x + 2y - 5z = -21

igreen · Answer

@kelseymanghamx Any options?

anonymous · Answer

Yes. Sorry. @iGreen. 
(2, 3, 5)

 (-2, 3, 5)

 (2, -3, 5)

 (2, 3, -5)

igreen · Answer

Okay, I never really learned this before, but we can plug the solutions into the three equations to find out our answer.

igreen · Answer

$x + 3y - z = 2$

$(2, 3, 5)$

$2 + 3(3) - 5 = 2$

$2 + 9 - 5 = 2$
$11 - 5 = 2$
$6 = 2$

6 does NOT equal 2. So the first option is wrong.

anonymous · Answer

I am not a strong math person, and I am trying to learn online. I'll help as best as I can. How do you know where to plug in the 3 numbers.

igreen · Answer

$x + 3y - z = 2$

$ (-2, 3, 5)$

$-2 + 3(3) - 5 = 2$
$-2 + 9 - 5 = 2$
$ 7 - 5 = 2$
$ 2 = 2$

This is true, now let's go to the second equation:

$x - 2y + 3z = 7$

$ (-2, 3, 5)$

$-2 - 2(3) + 3(5) = 7$
$-2 - 6 + 3(5) = 7$
$-2 - 6 + 15 = 7$
$-8 + 15 = 7$
$8 = 7$

This is FALSE, so we know Option B is wrong too.

igreen · Answer

The numbers in the options are in the order of (x, y, z). So look in the equation for x, y, and z then plug them in.

igreen · Answer

$x + 3y - z = 2$

$ (2, -3, 5)$

$2 + 3(-3) - 5 = 2$
$2 - 9 - 5 = 2$
$-7 - 5 = 2$
$-12 = 2$

This is also false, which leaves you with Option D.

anonymous · Answer

Thank you so much!
This is super helpful.

igreen · Answer

Sorry, I made a mistake on Option B.

igreen · Answer

Which is your answer..

anonymous · Answer

Option B is my answer?