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Can you look at a system of linear equations and tell how many solutions it has?

Can you look at a system of linear equations and tell how many solutions it has?. For example: Could you tell that the equations y=2x +1 and y= 2x-7 have no solution?. In this lesson you will learn to predict how many solutions a system of linear equations has by inspection.

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Can you look at a system of linear equations and tell how many solutions it has?

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  1. Can you look at a system of linear equations and tell how many solutions it has? For example: Could you tell that the equations y=2x +1 and y= 2x-7 have no solution?

  2. In this lesson you will learn to predict how many solutions a system of linear equations has by inspection.

  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. Assuming that all equations have one solution because those are the types of equations that are solved the most.

  7. There are three types of solutions for systems of linear equations One None Infinitely Many

  8. y = x - 5 y = 4x +4 y = 2x + 1 y = x - 3 y = 4(x+1) y = 3x + 1 Same Line infinitely many solutions Parallel lines no solution One point one solution

  9. Determine the number of solutions that the system has. Slope: -4, y-intercept: -16 y = -4(x+4) y = -4x-16 Slope: -4, y-intercept: -16 y = -4x-16

  10. Determine the number of solutions that the system has. Slope: 1, y-intercept: 1 y = x + 1 Slope: , y-intercept: 1 y = x + 1

  11. Determine the number of solutions that the system has. Slope: -5, y-intercept: 1 y = -5x + 1 Slope: -5, y-intercept: -2 y = -5x-2

  12. In this lesson you learned to predict how many solutions a system of linear equations has by inspection.

  13. How many solutions does the system of linear equations have? y= -2x+1 y= -2x-2

  14. How many solutions does the system of linear equations have? y= -3x+1 y= -2x-7

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

  16. What are the possible number of solutions for a system of linear equations?

  17. Does the system of linear equations y=2x and y=2x+1 have infinitely many solutions? Explain your answer.

  18. Create a second equation for the following system of equations so that they have one solution, no solution, and infinitely many solutions. • One solution • y = 7x + 1 y= • No solution • y = 7x + 1 y= • Infinitely many solutions • y = 7x + 1 y=

  19. How many solutions does the system of equations have? y=6(x+1) and y=6x+6 a) One b) None c) Infinitely Many How many solutions does the system of equations have? y=-3x and y=x+1 a) One b) None c) Infinitely Many

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