What does it mean to “break even”? Why is breaking even important? Bell Ringer What does it mean to “break even”? Why is breaking even important?

Exercise Ron and Harry are collecting Carger Coins. Right now, Ron has 12 and earns them at a rate of 2 a week. Harry does not have any Carger coins right now, but he earns them at a rate of 4 Carger coins a week. When will Ron and Harry have the same amount of Carger coins?

How did you do it?

How could we represent it on a graph?

What does your graph really mean? At 7 weeks, who will have more Carger coins? At 5 weeks, who will have more Carger coins?

The student will be able to: Objective The student will be able to: solve systems of equations by graphing. Designed by Skip Tyler, Varina High School

What is a system of equations? A system of equations is when you have two or more equations using the same variables. The solution to the system is the point that satisfies ALL of the equations. This point will be an ordered pair. When graphing, the solution is the point of intersection.

Steps to Solving a System of Equations By Graphing Graph each equation on same plane Step 2: Find the Point of Intersection Step 3: Check the point In summary…GRAPH IT, FIND IT, CHECK IT

Intersecting Lines The point where the lines intersect is your solution. The solution of this graph is (1, 2) (1,2)

Solve By Graphing (Ex 1) y=2x Check y=-x+3 (2) = 2(1) (2)= -(1)+3 (2) = 2(1) (2)= -(1)+3 2 = 2 2 = 2 Solution (1,2)

Solve By Graphing (Ex 2) x - y = -2 y = x + 2 Check x+y = 4 y = -x + 4 (1)-(3) = -2 (1)+(3)= 4 -2 = -2 4 = 4 Solution (1,3)

What is the solution of the system graphed below? (2, -2) (-2, 2) No solution Infinitely many solutions

Graph the equations. 2x + y = 4 (0, 4) and (2, 0) x - y = 2 Where do the lines intersect? (2, 0) 2x + y = 4 x – y = 2

Systems of Equations