how do you solve non-linear simultaneous equations?

Your reply is good for linear simultaneous equations, Pokemonfan88, but the question asked about non-linear simultaneous equations.  These are often more difficult to deal with.  There aren't really any general rules, especially if they are very complicated, but sometimes rearranging one to find one unknown in terms of another and substituting into another equation will give an equation that can be solved.  Often one needs to resort to numerical solution methods though.

If you have a specific set of non-linear simultaneous equations in mind Anonymous, post them here and we'll see what we can do.

To solve non-linear simultaneous equations, you must find the point at which they overlap. This can be done by finding the "x" and "y" values that apply to both equations.

Let's assume we have the following two simulatenous equations:

y = 3x

y = x + 12

We know that in each of these equations both "3x" (the same as 3 multiplied by x) and "x + 12" are equal to the variable of "y". Since the two equations are simultaneous, or occuring on the same graph, 3x and x + 12 must be equal. Thus, we can safely infer that:

3x = x + 12

Now we can simplify this equation using algebra. We can start by subtracting x from both sides to cancel out the "x" on the right side:

3x - x = x - x + 12

We can see that on the right side of the equation, "x - x" can be simplified to equal 0, so we can cancel that out to get:

3x - x = 0 + 12

or...

3x - x = 12

Also, we can simplify "3x - x" to give an  answer of "2x":

2x = 12

To simplify what we have now, we can divide each side by 2:

2x / 2 = 12 / 2

We can see that "2x / 2" is equal to "x" and that "12 / 2" is equal to 6, so we have a final answer of:

x = 6

Now that we know "x", all we have to do is find "y". This is really easy: we can just plug it into one of our first equations: "y = 3x" or "y = x+12". We'll do "y = 3x" for the sake of simplicity:

y = 3(6)

We can simplify "3(6)" by multiplying 3 and 6 to obtain an answer of 18, giving us our answer for "y":

y = 18

Points on a graph are shown as (x,y), so through using algebraic methods, we were able to find that the two equations intersect at the point (6,18).

If I didn't help you, I found a really helpful Purplemath page that further explains non-linear simultaneous equations you can see here.

-pokemonfan58