OH NO!! MATH!! Fine I will help you since you asked. Let me figure it out first its been a while.

First thing you will want to do is simplify this into two easier equations. There are multiple ways to do this, but I will show the easiest way.

31x + 12y – 24z = 105 -Equation 1

18x + 24y + z = 77 -Equation 2

12x – 6y + 4z = 5 -Equation 3

I numbered all of the equations, but dont get confused later when I make new equations. They are the simplified versions of two equations. Since you couldnt have given me easier numbers to work with. 🙁 First step is to simplify 2 equations into a simpler one and then simplify another 2 equations into a simpler one. Then do a linear equations against the two new ones. And… after all that, you get 1 variable. O_o

Dealing with Equations 2 & 3 – Lets Get rid of z

(Equation 2) * -4 = -72x – 96y – 4z = -308 : Equation 4

Add Equation 2 & 4-

(12x – 6y + 4z = 5) + (-72x – 96y – 4z = -308)

z’s dissapear : -60x -102y = 305 : Call this equation 5 — We need this equation later**

Dealing with Equations 1 & 2: Get rid of z’s

(Equation 2) * 24: 432x + 576y + 24z = 1848: Call this equation 6

Get rid of z’s by adding: Equations 1 & 6

(31x + 12y – 24z = 105) + (432x + 576y + 24z = 1848)

463x + 588y = 1953: Call this equation 7 — We need this equation also.

Combine equation 5 & 7. Hey look.. Its a two variable equation!!

-60x -102y = 305

463x + 588y = 1953

Since you asked about 3 variable equation I am guessing you already learned two variable equations. Basically from here.. Solve these two equations (I dont feel like it) and get the value for either x or y. Once you do that you can substitute this value into either the first, second, or third equation. Make two substitutions and you will have another two variable equations. Solve for one of the other variables. Once you have two of the variables.. Just substitute it again and you have the answer. Wow that took a while. Too check it, put all 3 values into any of the first three equations and make sure that they add up to the number on the other side of the equals sign. Good Luck understandign all this.

a million. remedy the 1st equation for y. y=a million-3x Now use this value of y interior the 2d equation 2x+(a million-3x)=5 a million-x=5 x=-4 Plug this value for x returned into an equation 3(-4)+y=a million y=13 (-4,13) 2. remedy the 2d equation for x (that’s less difficult than the 1st) x=4+3y Plug this into the 1st equation 3(4+3y)-9y=12 12=12 What? Now why did this happen? nicely look on the 1st equation: 3x-9y=12 each and every value is divisible by ability of three. in case you divide by ability of three you get: x-3y=4. the 2d equation! they’re the comparable equation so as that they are consistently equivalent! 3. remedy for y interior the 1st equation y=4x-8 Use this value interior the 2d equation 2x+(4x-8)=4 6x=12 x=2 Plug this returned into an equation 4(2)-y=8 y=-4 (2,-4)

if you doing these type of equations, i’m assuming that you have learned how to solve for mulitple variables.

You can use three methods:

1. Substitution method

2. linear combinations

3. or you can use matrix

try the Glenco text book web site or McGraw Hills

It’s a lot of work to write out explanations to solve this with matrices. Here’s a pretty good web site about solving this type of equation…

http://www.math.csusb.edu/math110/src/matrices/sol-sys.html

I really hope you also seek out extra help from a peer, teacher or tutor.