Systems of Three Equations

how do you write the solution?

(x, y, z)

when you have three systems with three variables, how do you solve it?

get rid of one of the variables so you end up with two equations and two variables

how do you know the order of variables when writing the system?

it goes in order of how it is in the equation; if you variables are x, y, and z, and they are read in that order in the equation, then that's how you will format them

what do you have to do if a system doesn't work?

solve it algebraically and prove that it doesn't work (where 2=0 or something)

same coefficient means ______, opposite coefficient means ______

subtract; add

why do you have to solve a system of three equations; why can't you just look on the graph?

the graph is 3-D, so it is practically impossible to tell

what do the intersections of three equations look like?

three planes intersect, where they ALL meet up at one or more points at the same place

what happens if one of the equations is missing a variable?

you can use that as one of you two other equations; solve the other two to get rid of said variable, and then solve further until you get those two variables, and then the final one.