1. What happens if we graph a system of equations and the lines are the same? y = 2(2x+4) y = 4x+8

2. In this lesson you will determine if a system of two linear equations in two variables has infinitely many solutions by graphing.

3. Let’s Review Slope Intercept Form of an Equation y = mx + b slopey-intercept

4. Graphing a linear equation y = 2x + 1 slopey-intercept

5. y = 2x + 1

6. A Common Mistake Thinking that all systems of equations must have one solution

7. Let’s Review Core Lesson Graph the system of linear equations. Determine their solution. y = 2(2x+4)y – 4x = 8 y = 4x+8 +4x = +4x y = 4x + 8

8. Let’s Review Core Lesson Graph the system of linear equations. Determine their solution. y = 2(2x+4) y = 4x+8 Slope: 4, y-intercept: 8 Slope: 4, y-intercept: 8 y = 4x+8

9. Let’s Review Core Lesson y = 2(2x+4) y = 4x+8 y = 4x+8

10. Let’s Review Core Lesson Graph the system of linear equations. Determine their solution. x -y = -1 y =x-2+3 y =x+1 -x =-x -y = -1-x -1 = -1 y= 1 +x y= x + 1

11. Let’s Review Core Lesson Graph the system of linear equations. Determine their solution. y =x+1 y =x-2+3 Slope:1, y-intercept: 1 Slope:1, y-intercept: 1 y =x+1

12. Let’s Review Core Lesson y =x-2+3 y =x+1 y =x+1

13. In this lesson you learned to determine if a system of two linear equations in two variables has infinitely many solutions by graphing.

14. Let’s Review Guided Practice Find the solution for the system of linear equations y-3x = 3 and y = 3(x+1) by graphing.

15. Let’s Review Guided Practice y-3x = 3 y =3(x+1)

16. Let’s Review Guided Practice y =3(x+1) y-3x = 3

17. Let’s Review Guided Practice Find the solution for the system of linear equations y=2x-2+4 and y=2(x+1) by graphing.

18. Let’s Review Guided Practice y=2x-2+4 y= 2(x+1)

19. Let’s Review Guided Practice y=2x-2+4 y= 2(x+1)

20. Let’s Review Extension Activities When we solve the systems of equations y=2x+2 and y=2(x+1), what is our solution? What does it mean?

21. Let’s Review Extension Activities How many solutions does the system of equations y=-3x-3 and y=-3(x+1) have? Why?

22. Let’s Review Extension Activities Create a system of linear equations that have infinitely many solutions.

23. Let’s Review Quick Quiz The solution for the system of linear equations y=2x+1 and y=2x-3 is? a) One solution b)Infinitely Many Solutions The solution for the system of linear equations y=4x-12and y=4(x+3)is? a) One solution b) Infinitely Many Solutions