Question

simultaneous equations with 3 variables. I kinda know what to do but I keep getting them wrong, so maybe I don't. Okay, 3 problems.
3x + y + 2z = 5
x - y - z = 0
2x + 3y = 2
What is x, y, z?

Answer 1

x=1,y=0,z=1

Answer 2

we can use gauss elimination method to solve it

Answer 3

add the first 2 equations=>
4x+z=5
now multiply the second by 3 and add it to the 3rd.
5x-3z=2

now solve for x and z:z=5-4x
=>5x-3(5-4x)=2
17x=17=>x=1
z=1
substitute in any of the equations to find y:
3+y+2=5
=>y=0
(x;y;z)=(1;0;1)

Answer 4

okay just looking through your answer... thanks...

Answer 5

okay cool hmmm I must be making little errors because my method seems ok... ah there are so many little calculations... well thankyou :)

Answer 6

this is how i do it:
choose any 2 of the equations to eliminate one variable
choose other 2 equations to eliminate the same variable
you end up with 2 equations in 2 unknowns,which you can solve easily.
you can then find the eliminated variable from any of the 3 equations

Answer 7

Or you can use cramer's rule.

Answer 8

Cramers rule?

Answer 9

it involves matrices and determinants to solve a system of equations:
http://www.occc.edu/maustin/cramers_rule/cramer%27s%20rule.htm

Answer 10

Oh okay I'll look forward to it when I get to matices :) Thanks

Answer 11

haha oh dear it looks complex...

Answer 12

Well, if you haven't been introduced to linear algebra yet, then I think solving systems by elimination and substitution will suffice.