Definitions: A linear equation in one unknown is an equation of the form a x = b, where a and b are constants and x is an unknown that we wish to solve for. Similarly, a linear equation in n unknowns x_{1}, x_{2}, …, x_{n} is an equation of the form: a_{1} · x_{1} + a_{2} · x_{2} + … + a_{n} · x_{n} = b,where a_{1}, a_{2}, …, a_{n} and b are constants. The name linear comes from the fact that such an equation in two unknowns or variables represents a straight line. A set of such equations is called a system of linear equations. 
In this method we simply draw graphs of the equations as we have done to the right. Notice that the graph of each equation is a straight line. (This is characteristic of a linear system. There are no curves, only straight lines.)
This system of equations is inconsistent because there is no way that x + y can equal 2 and 4 at the same time. As shown to the right, the graph of this system consists of two parallel lines that never cross. Thus there is no solution.
This system is redundant because the second equation is equivalent to the first one. The graph consists of two lines that lie on top of one another. They “cross” at an infinite number of points, so there are an infinite number of solutions.
Counting equations and unknowns These results can be generalized to linear systems of equations with any number of equations and any number of unknowns:
