Question

Help:
y=x^2
x=z+y
z=4x+y
Solve x+y+z =?

Answer 1

In terms of what should we give our answer?

Answer 2

May you please explain what you mean by terms?
If you mean something like form, I think it's supposed to be simplified as far as possible, whether there are variables left over or no.

Answer 3

I guessed 2x^2+8x+2y, but I'm not sure...

Answer 4

In terms of what means, what variables should our expression contain
Example
4xy (given in terms of x and y)
4x^2 (given in terms of x)
4yz (given in terms of y and z)

Answer 5

terms are formed by numbers/letters multiplied together (no add or subtract)

adding
y=x^2
x=z+y
z=4x+y

is , in some sense, simple: you put a "+" sign between each term to show them being added together:
x+y+z = x^2 + y+z + 4x+y

However, they usually mean add, and simplify as much as possible.
in this case we have 2 y's y+y which is 2y

x+y+z = x^2 + 4x + 2y + z

Answer 6

This is a system of homogeneous equations, where there is the trivial answer of
x=0,y=0,z=0.
However, there is also a set of non-trivial solutions. If you can solve for the numerical values of x,y and z, then you can easily find x+y+z.
You can solve by substitution or a combination of any other techniques.

Answer 7

Hint:
the non-trivial solution has all rational values, y>0 (obviously), and the other two are negative fractions. The sum x+y+z is a negative integer.