Systems of Equations. Substitution

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An equation in two variables X and Y is linear if the exponent of both of them is one. But, be careful "one over X" is "X raised to the negative one", the "square root of X" is "X raised to the one half". The solution of a system of two linear equations on two unknowns X and Y is the set of values of X and Y that satisfy both equations at the same time. That is, the set of points (X,Y) on the plane that satisfy both equations.

The graph of a linear equation on two variables is a straight line. If both lines intersect, the system of equations has a unique solution. If they are parallel, the system has no solution. If both lines coincide (one on top of the other) there are infinite solution (infinite points of intersection).