Question

Solve the system of equations.

x + y + z = 18
3x + 4y + 5z = 72
x + z = 8

Answer 1

hmmm no clue :3 srry mate

Answer 2

is there something missing in the last one or is it just \(x+z=8\)?

Answer 3

@satellite73 - it's just x + z = 8

Answer 4

yeah it is probably what you wrote
this is donkey work, let the computer do it
http://www.wolframalpha.com/input/?i=+x+%2B+y+%2B+z+%3D+18%2C+3x+%2B+4y+%2B+5z+%3D+72%2C+x+%2B+z+%3D+8

Answer 5

looks like you get \((4,10,4)\)

Answer 6

we can do it by hand if you like, but it is not worth the aggravation imho

Answer 7

Thanks, but to get credit for the problem in my class, I need to show my work. Sorry.

Answer 8

ok then multiply the first equation by \(-4\) and add it to the second

Answer 9

\[ x + y + z = 18\\
3x + 4y + 5z = 72\] becomes
\[-4x-4y-4z=-72\\
3x+4y+5z=72\]

Answer 10

add them up, get
\[-x+z=0\] and you also have the last equation
\[x+z=8\]
solve
\[-x+z=0\\
x+z=8\] by addition, get \[2z=8\\
z=4\]

Answer 11

now that you have \(z\) you can find \(x\) easily, then you can find \(y\)

Answer 12

you good from there?

Answer 13

@satellite73 - I don't think so.... Sorry. Let's say I plug in z into the first equation. I would get x + y = 14. What do I do with this equation?

Answer 14

we're good with \(z=4\) right?

Answer 15

the last equation is \(x+z=8\) so if \(z=4\) we have \[x+4=8\\x=4\]

Answer 16

now that you have \(x=4,z=4\) put those in either of the first two equations to find \(y\)

Answer 17

@satellite73 - Oh okay, I get it now.

If I use the first equation; x + y + z = 18 and plug in x and z,
4 + y + z = 18
y = 10.

Answer 18

yup

Answer 19

@satellite73 - Thank you so much!

Answer 20

yw