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In a nonlinear equation, each variable must only have one solution.
The answer depends on the equation!
Several methods exist. For example: solve one equation for one variable, replace that variable in the other equation. (Two simultaneous equations will often have two variables each.)
Select any three values of x in the domain of the equation. Solve the equation at these three points for the other variable, y. Then each (x, y) will be an ordered pair that is a solution of the equation.
Typically, you'll solve such an equation for one variable, in terms of the other variable. For example: y = 3x + 2 y = x squared - 5 y = 5 sin 3x Each of these is already solved for "y". If you substitute any value for "x" in this solution, you can calculate the corresponding value for "y".