Pre-Calculus 11: Section: 8.1 Solving Systems of Equation by Graphing

Review) Graphing a Linear Function When given a linear function in the form of y=mx+b The “m” is the slope and the “b” is the y-intercept Ex: Graph the line: Start at the y-intercept Suppose the equation was in general form: Isolate the Y-variable to get it into standard form: Then apply the slope to find other points: Connect the dots

I) Solving a Linear System: In this section, you will be given a system with two equations where each one is a different graph “Solving” a system of equation means you are finding the “points of intersection” – where the two graphs meet The coordinates of the “intersection points” will satisfy both equations in the system When you plug the solution into the original equation, both sides will be equal 2 separate Lines A Line with a Parabola Two Separate Parabolas

Ex: Solve the System by Graphing Isolate “y” in each equation Graph each equation x y -9 -8 -7 -6 -5 -4 -3 -2 -1 1 2 3 4 Make a table of Values if the y-intercept is off the graph The Intersection is:

Practice: Solve the System by Graphing Isolate “y” in each equation Graph each equation x y -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 8 9 10 11 Parabola Vertex (0,2) a =1  1,3,5,7 The Intersections are:

Practice: Solve the System by Graphing Isolate “y” in each equation Graph each equation x y -6 -4 -2 2 4 6 Parabola Vertex (2,-3) a =1  1,3,5,7 The Intersections are:

Ex: Solve the System by Graphing -4 -2 2 4 6 8 10 -6 This is called the point of tangency. The Intersection is:

Ex: Solve the System by Graphing -6 -4 -2 2 4 6 8 The Intersections are:

Homework: Assignment 8.1