1. ## basic equations

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.

2. Originally Posted by brandilee
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.
$18x + 24y + z = 77$

$z = 77 - 18x - 24y$

$12x + 6y + 4(77 - 18x - 24y) = 5$

$12x + 6y + 308 - 72x - 96y = 5$

$-60x - 90y = -303$

$y = \frac{303 - 60x}{90}$

$31x + 12y - 24z = 105$

$31x + 12( \frac{303 - 60x}{90} ) - 24z = 105$

$2790x + 303 - 60x - 2160z = 9450$

$2730x+303-2160( 77-18x-24( \frac{303 - 60x}{90} )) = 9147$

$2730x - 166320 + 38880x + 174528 - 34560x = 9147$

$7050x = 939$

$x = 0,1331914894$

You should be able to continue from here, but check my calculations though.

3. sorry, i wrote that wrong
the last equation is 12x-6y+4z=5
im still having trouble following what you did

4. Try using Cramer's rule, in my opinion its quicker and easier than double elimination or substitution.

5. Originally Posted by brandilee
sorry, i wrote that wrong...
You have got to be kidding me

Originally Posted by SnipedYou
Try using Cramer's rule, in my opinion its quicker and easier than double elimination or substitution.

Do what he says... I only know the substitution and elimination method as of yet.

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EDIT: Cramer's Rule

6. i checked out cramers rule, and have no idea how to use it. thats a little beyond what ive learned so far. this is so frustrating. my class is all online, so theres no real help from teachers

7. Originally Posted by brandilee
i checked out cramers rule, and have no idea how to use it. thats a little beyond what ive learned so far. this is so frustrating. my class is all online, so theres no real help from teachers
Do you know how to do equations that only have 2 variables? Like only x and y, and no z?

8. yeah usually

9. Originally Posted by brandilee
yeah usually
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.