Nash

Graphing Systems of Equations By Mark, Joseph, Austin, and Samuel The graph shown above is an example of a system of equations with no solution. This is because both equations have the same slope, but different y-intercepts. As you can see on the graph, the lines are parallel to each other when they are graphed. Moving along, here we have an example of a system of equations with one solution shown below. By looking at the equations in the picture below, you can see that they have different slopes and y-intercepts. When the equations are graphed, you can see that the lines intersect at one point with each other and you have to check that one point to see if it makes both of the equations true. The example shown above is a system of equations with infinitely many solutions. This shows that both of these equations have the same slopes and y-intercepts. Therefore, they have the same line on the graph shown above and any point on the line is a solution to the system.
 * //__Vocabulary Words to Learn From This Lesson__//**
 * 1) __**System of linear equations**__- a system made up of two or more linear equations.
 * 2) __**Solution of the system of linear equations**__- any ordered pair in a system that makes all the equations true**.**
 * 3) __**No solution**__- when a system of linear equations have a graph with parallel lines.
 * 4) __**Infinitely many solutions**__- when a system of linear equations have a graph with the same line.
 * We hope that you find this page very useful on how to graph systems of equations and that concludes this lesson. Thank you for taking the time to view this page.​**