How can a system of two linear equations be solved?

There are, mainly, three ways of doing it easily:
Substitution: It consists in modifying one of the equations in such a way that x is expressed in terms of y  (or y in terms of x) and then substitute that expression in the other equation. Elimination: it consists in multiplying on of the equations by a number such that when we add both equations x or y disappear, getting one equation with one variable easy to solve. Then, we substitute that solution into one of the equations. Graphically: it consists in drawing both lines, each one represented by one equation, and find out the point that have in common.