Given the system of equations, solve for x,y,z.
2x + y + z = 6
x + 2y + z = 12
x + y + 2z = 24
Thanks!
Subract the first two equations from one another
$\displaystyle 2x+y+z=16$
$\displaystyle -(x+2y+z)=-12$
$\displaystyle =x-y=4$
solve for x in the equation
$\displaystyle x=y+4$
go back and substitute for x and reapeat the process until you have completely solve the system.
Does that help?
Make your life easier and simplify where you can.
$\displaystyle (x + y + 2z) - (x + 2y + z) = 12$
$\displaystyle z - y = 12$
$\displaystyle (x + 2y + z) - (2x + y + z) = 6$
$\displaystyle y - x = 6$
$\displaystyle (x + y + 2z) - (2x + y + z) = 18$
$\displaystyle z - x = 18$
Now just keep substituting.
$\displaystyle x + y + 2z = 24$
$\displaystyle (z - 18) + (z - 12) + 2z = 24$
$\displaystyle 4z - 30 = 24$
$\displaystyle z = \frac{27}2$