What do I do when I do an equation with 3 variables and I keep getting z=z?

Question

The equation is:
x+y= 6
x+z= -2
y+z= 2

I keep getting z=z and I don't know what to do.
Any help would be awesome!
Thanks.

What am I suppost to do?
What does z equal (as in what number does z equal), because I have no idea what to do?

I am suppost to find what x y and z equal

Answer 1

take the first equation and subtract the second from it:

x+y=6
-x-z=2

which will get you: y-z=8

take that equation and add that to the third equation:

y-z=8
y+z=2

that will give you 2y=10

divide by 2 and you get y=5

plug that into the third original equation and you get 5+z=2 and so you know z=-3..

plug y=5 into the first original equation and you get x+5=6 and so you know x=1

and thus: x=1, y=5, and z=-3

Answer 2

I'm glad because I haven't done math exercises (I'm 26), and apparently I found the right answer.

First, you need to find a "formula" which will help you find the answer for ONE letter.

So, I chose that one:
x + y = 6
y + z = 2

So: [(x + y) + (y + z) = 6 + 2] this line is just to show you
x + 2y + z = 6+2
x + 2y + z = 8
x + z = 8 - 2y
- 2 = 8 - 2y
2y = 8 + 2
y = 5

Then, just replace "y" by "5" in the other formulas.

x = 1
z = -3

Answer 3

First find everything in terms of x
x = 6-y
y = 2-z so x=6-(2-z)
z = -2 - x so x= 6 - (2 - ( -2 -x)) then simplify x = 6 - ( 2 + 2 +x) then x = 6 - 4 - x bring the Xs to one side and 2x = 2 or x=1
from that you know that y = 6 - x or y = 6 - 1 or y = 5 and
z = 2 - y or z = 2 - 5 or z = -1
so you end up with x = 1, y = 5, and z = -1

Hope that helps

Answer 4

take the 3rd equation, solve for z:

z= 2- y

plug in z into the 2nd equation to find x:

x+ (2-y) = -2

x= -4 + y

plug this into the top equation to find y:

(-4+y) + y = 6

-4 + 2y = 6

2y = 10

y =5

so if y = 5, then plug it in to find z:

5+ z = 2

z = -3

plug y into 1st equation: x + 5 = 6

x = 1

check: x+ y = 1 + 5 = 6 check!
check: x+ z = 1 + (-3) = -2 check!
check y + z = 5 + (-3) = 2 check!

:)

Answer 5

because z does equal z!

OK, solve #1 for x... x = 6-y

substitute in #2 and solve for y... (6-y) + z = -2, y = 8 + z

substitute in #3 (8+z) + z = 2,

z = -3

y = 5

x = 1

Answer 6

y=x+4 because the diff between x+z=-2 and y+z=2 is 4.
x+x+4=6
x=1
z=-3
y=5

Answer 7

x=6-y
x=-z-2

6-y=-z-2
8-y+z=0

z= -8+y
z= 2-y

-8+y = 2-y

2y = 10

y=5

x+5=6
x=1

1+z=-2
z=-3

Answer 8

I haven't done math in a while, but....

z=2-y
x=6-y
so... (6-y)+(2-y)=-2
8-2y=-2
y=-10/-2=5
x+5=6, x=1
z=-4

Answer 9

alright, x is 1, y is 5, and z is -3, I don't really know how to figure it out, but that's the answer. Good luck

Answer 10

I'm sorry, I don't know what to do with this. I tried several ways, and keep getting 4= -2, or -4=6. Are you sure it is possible? NEVER MIND. I'm wrong. the answer after me looks right.