Objective: Solve systems of two linear equations by graphing.
A system of equations is a set of two or more equations that are to be solved simultaneously. A solution of the system of equations must also be a solution of every individual equation contained in the system.
While systems vary widely in terms of the number and type of equations they contain, this course will focus primarily on systems of two linear equations. One way to visualize the solution of a system of two linear equations is to look at a graph of the equations and identify the point at which the lines intersect. Watch the video below to see how this process works.
When two linear equations are graphed, three possibilities exist. First, the lines may intersect, which means that the system has one solution--namely, the point of intersection. Second, the lines may be parallel, which means that the system has no solutions. Third, the if the two equations are equivalent, they will produce the same line, which means that the system has an infinite number of solutions, since every point on the line is a solution to both equations. These possibilities are summarized in the table below.
Watch the video below to see examples of how to solve of each type of system by graphing.
Complete the worksheet attachment below and then check your answers using the solutions attachment. Once you have completed these exercises, click the link to advance to the next lesson.