Question

Consider this equation in x, y, and z:
7 = 3x + 2y - z

How many more equations would you need to solve x, y, and z? In which variables can the additional equations be? Give examples of equations that would help solve these variables.

Answer 1

you have 3 variables so you need 3 equations

Answer 2

but what would they be, how would i figure out what the equations would be?

Answer 3

the other 2 equations can anything

Answer 4

ex. x=1, y=1
or x=y, y=1,
or x+y=100, y+z= 1000
or x+y-z=-100000, z=1

Answer 5

how would those equations help to solve for x,y and z though?

Answer 6

through the use of substitution or elimination method...

Answer 7

so are you creating a system of equations by putting more equations in there?

Answer 8

short answer, YES

what you're given is a single equation
a system of equation refers to more than 1 equation
that could mean 2 equations or 3 equations or 100 equations

Answer 9

they're sort of classified by the number of equations and the number of variables

ex. "2 equations 2 unknowns"
"5 equations 4 unknowns"

general rule of thumb, if the number of variables is more than the number of equations then you cannot completely solve the system of equations

if the number of variables are less than the number of equations, then
a. something is wrong
b. one of the equations are repeated

ex.
x+y=1 is the same as 2x+2y=2

Answer 10

to completely solve for a system of equations, you need at least "n equations n unknowns"

the number of equations must be equal to the number of variables

note the word AT LEAST