There are two common algebraic methods for solving system of linear equations: substitution and elimination. Graphical method is also considered for the case of system of two linear equations as it is helpful for better understanding of the concept of solution of a system.

Graphical method

Here, given system of two linear equations, we use the graphs of both equations to identify the solution of the system. As you have seen in Unit 7, the graph of ax + by = c is a straight line. In particular, rearrange this equation, you can see that

Which is an equation of the line with slope

and y-intercept

Recall also that every ordered pair (x, y) of points that lie on this line satisfy the equation of the line.

So, a system of two linear equations a₁x + b₁y = c₁ and a₂x + b₂y = c₂ has two straight lines given by

ordered pair (x, y) corresponding to the point of intersection of these lines satisfy both equations. Therefore, this ordered pair is a solution of the system.