how do you solve this multi-variable problem?

Question

The problem is 2x+y=80. idk if i need to solve for x or y.

Answer 1

you need two equations if you want to solve for x and y. But if you just want y in terms of x then:

y = 80 - 2x

Or x in terms of y:

2x = 80 - y
x = 40 - y/2

Answer 2

It can't be solved, has an *infinite* number of solutions.

In order to find specific values for x and y, you need another equation, which is unique from the first.

For an example, if the second equation were, say:

x+2y = 42,

Then you could solve by "substitution," rearranging:

y = 21 - (1/2)x

then substituting 21 - (1/2)x for y into the first equation:

2x + y = 80

2x + { 21 - (1/2)x } = 80

(3/2)x = 59

x = 118/3

then, substituting 118/3 for x into the first:

2y + x = 80

2y + (118/3) = 80

y + 118/6 = 40

y = 61/3.

So the only possible values that can satisfy *both*

2x + y = 80,
x + 2y = 42

are x = 118/3, and y =61/3.

Don't write that on your homework! This is just an *example* of how to solve, provided you actually have that second equation!

I already pointed out that you don't have the other equation, therefore there are an infinite number of solutions, that satisfy the first equation.

In order to solve for 2 variables, you need at least 2 unique equations! To solve for 3 variables, you would need 3 equations; 4 equations for 4 variables, etc.

Hope that makes sense,
W.O.M.B.A.T.

Answer 3

you need more information to find a real solution. you can solve for each and will get a function