8.1 Notes - Systems_of_Linear_Equations_in_Two_Variables

8.1 Notes - Systems_of_Linear_Equations_in_Two_Variables -...

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Systems of Linear Equations in Two Variables A system of linear equations is just two or more equations that are graphed on the same graph. A solution to a system of equations is the point (or points) that are on both lines. To determine if an ordered pair is a solution, plug the values of the coordinates into each equation. If they work in both , then that point is on both lines and it is a solution . When two straight lines are graphed on the same graph, one of three things will happen: The lines intersect in a single point. That point of intersection is the solution of the system of equations. We call this system consistent and we call the equations independent . The lines are coincident. That means that when we graph the second equation, it lies right on top of the first line. These lines have an infinite number of points in common. We call this system consistent and we call the equations dependent . The lines are parallel . They have no point of intersection. There is no solution to this system of equations. We call this system
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