The systems of the linear equations are solved by means of matrixes. For the systems of the nonlinear equations there is no general algorithm of the decision. However application of some methods can help.
Instruction
1. Try to lead one of the equations to a good view, that is, to it in which one of unknown easily says through another. For example, the equation (x²-2y²) / by the first consideration seems to xy=2 difficult. However it is possible to notice that at x≠0, it is equivalent to y≠0 x²-2y²=2xy that finally is given to a quadratic equation x²-2xy-2y²=0. It is easy to factorize the left part: x ²= (x-3y) (x+y). Now it is possible to express one variable through another, the equation (x-3y) =0 gives (x+y) set of decisions x-3y=0, x+y=0. It was necessary to substitute result in other equation of a system and to solve it.
2. Sometimes in externally terrible systems of the nonlinear equations formulas of abridged multiplication are disguised: sum square, difference square, sum cube, difference cube, difference of squares and others. It is necessary to be able to see them. Try to put and subtract the system equations with each other. You remember as well that multiplication of both members of equation by the same number remains faithful equality. It too in certain cases can help to find a solution.
3. Try to spread out any of the equations to linear multipliers. Try to solve it as the quadratic equation is relative one of unknown. Suddenly the discriminant will be a full square? It considerably will simplify a task, then by search of roots of a quadratic equation you will be able to get rid of the sign of a square root.
4. Sometimes the method of replacement of variables works. But here, of course, to pick up suitable replacement happens very difficult. Especially successful replacement can make a system trivial. Only at the end do not forget to find and write down the answer for initial sizes since in the course of the decision it is often forgotten that it is required to find.