6-1 Solving Systems by Graphing System of Linear Equations Two or more linear equations. Solution of a System of Linear Equations Any ordered pair that makes all of the equations in a system true.

6-1 Solving Systems by Graphing Consistent System A system of linear equations that has at least one solution. A consistent system can be either independent or dependent. Independent System Any consistent system that has exactly one solution. Dependent System Any consistent system that has infinitely many solutions. Inconsistent System A system of linear equations that has no solution.

6-1 Solving Systems by Graphing A system of linear equations can be used to model problems. Systems of equations can be solved in more than one way. One method is to graph each equation and find the intersection point, if one exists.

6-1 Solving Systems by Graphing What are the Properties of Systems of Linear Equations? If lines in a system of equations intersect: The equations have one point in common so system has one solution. The lines intersect at one point. The lines have different slopes. The equations are consistent and independent.

6-1 Solving Systems by Graphing What are the Properties of Systems of Linear Equations? If the lines in a system of equations are parallel: The equations have no points in common so the system has no solution. The lines are parallel. The lines have the same slope and different y-intercepts. The equations are inconsistent.

6-1 Solving Systems by Graphing What are the Properties of Systems of Linear Equations? If the lines representing the equations are the same line: The system has an infinite number of points in common, so it has an infinite number of solutions. The lines are the same. The lines have the same slope and y-intercept. The equations are consistent and dependent.