Graphing Linear Systems Worksheets

How to Graph Linear Systems - A system of linear equation comprises two or more linear equations. The solution of a linear system is the ordered pair that is a solution to all equations in the system. One way of solving a linear system is by graphing. The solution to the system will then be in the point in which the two equations intersect. It's a good idea to always check your graphical solution algebraically by substituting x and y in your equations with the ordered pair. A linear system that has exactly one solution is called a consistent independent system. Consistent means that the lines intersect and independent means that the lines are distinct. Linear systems compose of parallel lines that have the same slope but different y-intersect do not have a solution since the lines won't intersect. Linear systems without a solution are called inconsistent systems. Linear systems composed of lines that have the same slope and the y-intercept are said to be consistent dependent systems. Consistent dependent systems have infinitely many solutions since the lines coincide.

Fun Fact

In correspondence with Fermat, Blaise Pascal laid the foundation for the Theory of Probability.