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.
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By the substitution method By the elimination method By plotting them on a graph
"A slogan for the elimination method in algebra could be 'Combine and conquer!' This highlights the strategy of adding or subtracting equations to eliminate variables. For the substitution method, a slogan like 'Swap and solve!' could emphasize the idea of substituting expressions to find the solution."
By solving the simultaneous equations the values of x and y should be equal to the given coordinate
The gaussian elimination is used to solve many linear equations with many unknown varaibles at once. [See related link below to find out how to do it]. This is used alot by engineers you know ceratin variables in there structures and want to find out what the stress and strain is in certain areas. They make up there linear equations and then they can use the gaussian elimination method to find the unknown variables.
That is the same as solving the equation. There is no single and simple method to solve ANY equation. You have to learn lots of different methods, to solve different types of equations. You might start by picking up an algebra book - to a large part, such books deal with the topic of solving equations.