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What happens if we graph a system of equations and the lines are the same?

What happens if we graph a system of equations and the lines are the same?. y = 2(2x+4). y = 4x+8. In this lesson you will determine if a system of two linear equations in two variables has infinitely many solutions by graphing. Slope Intercept Form of an Equation. y = mx + b. slope.

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What happens if we graph a system of equations and the lines are the same?

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  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. Slope Intercept Form of an Equation y = mx + b slope y-intercept

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

  5. y = 2x + 1

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

  7. 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. Graph the system of linear equations. Determine their solution. Slope: 4, y-intercept: 8 y = 2(2x+4) y = 4x+8 Slope: 4, y-intercept: 8 y = 4x+8

  9. y = 2(2x+4) y = 4x+8 y = 4x+8

  10. Graph the system of linear equations. Determine their solution. x -y = -1 y =x-2+3 -x =-x y =x+1 -y = -1-x -1 = -1 y= 1 +x y= x + 1

  11. Graph the system of linear equations. Determine their solution. Slope:1, y-intercept: 1 y =x+1 Slope:1, y-intercept: 1 y =x-2+3 y =x+1

  12. y =x+1 y =x-2+3 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. Find the solution for the system of linear equations y-3x = 3 and y = 3(x+1) by graphing.

  15. y =3(x+1) y-3x = 3

  16. y-3x = 3 y =3(x+1)

  17. Find the solution for the system of linear equations y=2x-2+4 and y=2(x+1) by graphing.

  18. y= 2(x+1) y=2x-2+4

  19. y=2x-2+4 y= 2(x+1)

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

  21. How many solutions does the system of equations y=-3x-3 and y=-3(x+1) have? Why?

  22. Create a system of linear equations that have infinitely many solutions.

  23. 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

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