Question

Solve the system by substitution
2x-y+z=-4
z=5
-2x+3y-z=-10

Answer 1

Add `2x-y+z=-4` and `-2x+3y-z=-10` to each other.
This will eliminate x and z variables.

Answer 2

\(\large\color{black}{ \displaystyle 2x{~~~~}-y{~~~~}+z{~~~}={~~}-4 }\)
\(\Large\color{red}{+}\)
\(\large\color{black}{ \displaystyle -2x{~~}+3y{~~}-z{~~~}={~~}-10 }\)
\(\large\color{blue }{ \displaystyle ^\text{_________________________________} }\)

Answer 3

Well I have multiple choice
A.(-8,7,5)
B.(-8,-7,5)
C.(8,-7,5)
D.(-8,-7,-5)
I think it is C?... What do you think? @SolomonZelman

Answer 4

I try not to think about the options, rather help you solve the equation.

Answer 5

okay could you please hold on a sec while I solve it @SolomonZelman

Answer 6

I got...
x+2y=-14
@SolomonZelman

Answer 7

2x+(-2x)= what?

Answer 8

4 - 4 = 0
(Quantity) - (Quantity) = 0

Answer 9

2x+(-2)=0x

Answer 10

yes, so you should get:
2y=-14,
from the addition of the two equations

Answer 11

Can you solve for y?

Answer 12

okay so then would I divide 2 from -14 to get y?
-14/2=-7

Answer 13

yes, so y=-7,
and you are given that z=5.

Answer 14

use the first equation:
2x-y+z=-4

and use the fact that you know that y=-7 and z=5,
to solve for x.

Answer 15

I got x=-8

Answer 16

x=-8,y=-7, and z=5

Answer 17

2x-(-7)+5=-4
2x+7+5=-4
2x+12=-4
2x=-16
x=-8

Yes, beautiful !!

Answer 18

And that is indeed the correct final answer:

Answer 19

Yay! Thank you for your help :)