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When is it possible for an ordered pair to be the solution of more than one equation?
Always. Every ordered pair is the solution to infinitely many equations.
If a system of equations is independent how many soultions will it have?
A system of equations may have any amount of solutions. If the equations are linear, the system will have either no solution, one solution, or an infinite number of solutions. If the equations are linear AND there are as many equations as variables, AND they are independent, the system will have exactly one solution.
When solving a system of equations by elimination you find what?
You find a solution set. Depending on whether the equations are linear or otherwise, consistent or not, the solution set may consist of none, one, several or infinitely many possible solutions to the system.
What does the solution represent when a system of equations has a single solution?
The graphs of the two equations have only one intersection point.
What is numerical solutions of nonlinear equations?
Linear equations, if they have a solution, can be solved analytically. On the other hand, it may not always be possible to find a solution to nonlinear equations. This is where you use various numerical methods (eg Newton-Raphson) to work from one approximate numerical solution to a better solution. This iterative procedure, if properly applied, gives accurate numerical solutions to nonlinear equations. But as mentioned above, they are not arrived at analytically.
