Question

Find the complete solution for the linear system if possible.

x + y + z =8
x + 2y + 2z =14
x + y - z =2

Answer 1

subtract the third equation from the first and post what you get.

Answer 2

0+0-2z=-6

Answer 3

?

Answer 4

right. so if -2z = -6, then z=?

Answer 5

3

Answer 6

ok good.
substitute that in the first equation

Answer 7

x+y+3=8?

Answer 8

yes, so x+y =?

Answer 9

5

Answer 10

okay now look at the 2nd equation
x+2y+2z=14
you know that z=3
x+2y = 8
x+y+y=8
you know that x+y = 5
5+y =8

Answer 11

so what would the final answer be written like?

Answer 12

what is y?

Answer 13

3

Answer 14

and therefore x =?

Answer 15

not sure

Answer 16

x+y=5, right?

Answer 17

yes

Answer 18

so plug in 3 for y giving you x =2

Answer 19

?

Answer 20

right. you have your answer