solve for x,y, and z
31x+12y-24z=105
18x+24y+z=77
12x+6y+4z=5
ive tried doing this several ways, but i get different answers every time. all i am able to really do is get rid of y by multiplying the 3rd equation by 4. after that im just kind of stuck.
You have got to be kidding me
Do what he says... I only know the substitution and elimination method as of yet.
---------------------
EDIT: Cramer's Rule
Let's say you have the following(Only for explanatory purposes):
x + y + z = 3 --- (1)
2x + 2y + z = 6 --- (2)
x + y + 2z = 9 --- (3)
Take equation (1)
Isolate z:
z = 3 - x - y --- (4)
Now take (4) and plug it into (2)
2x + 2y + (3 - x - y) = 6
x + 2y + 3 - x - y = 6
x + y = 3
y = 3 - x --- (5)
Now take your new equation and plug that into (3)
x + y + 2z = 9 --- (3)
BUT you know that [ y = 3 - x --- (5) ] AND [ z = 3 - x - y --- (4) ]
Take [ z = 3 - x - y --- (4) ] again:
z = 3 - x - (3 - x)
z = 3 - 3 - x + x = 0
x + (3 - x) + 0 = 9
3 = 9
Okay, notice this doesnt work out, it's because I used made up equations and numbers, but this will be the proecedure you'll have to follow.