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Systems with No Solution or Infinitely Many Solutions

Systems with No Solution or Infinitely Many Solutions. September 15, 2014 Pg. 21 in Notes. Warm-Up (pg. 20). Solve the following system of equations using the elimination method. 7x + 4y = 2 9x – 4y = 30 Questions on Friday’s Assignment?. No Solution/Infinitely Many Solutions.

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Systems with No Solution or Infinitely Many Solutions

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  1. Systems with No Solution or Infinitely Many Solutions September 15, 2014 Pg. 21 in Notes

  2. Warm-Up (pg. 20) • Solve the following system of equations using the elimination method. • 7x + 4y = 2 • 9x – 4y = 30 Questions on Friday’s Assignment?

  3. No Solution/Infinitely Many Solutions • Title: page 21

  4. Essential Question • How do you know if a system has one solution, no solution, or infinitely many solutions?

  5. Systems with One Solution • Solution will be an ordered pair.

  6. Systems with No Solution (NS) • When solving, statement is untrue. • Example: y = 3x + 1 6x – 2y = 5 Let’s use substitution: 6x – 2(3x + 1) = 5 6x – 6x – 2 = 5 -2 = 5 The variable canceled and this statement is untrue, so this system has no solution.

  7. Systems with Infinitely Many Solutions • When solving, statement is always true. • Example: 2x + 3y = 6 -4x – 6y = -12 Let’s use elimination: 8x + 12y = 24 -8x – 12y = -24 0 = 0 Each term canceled and this statement is always true, so this system has infinitely many solutions.

  8. Practice – Determine whether each of the following systems of equations has one solution, no solution, or infinitely many solutions. • 24x – 27y = 42-9y + 8x = 14 • 3/2 x + 9 = y4y – 6x = 36 • 7y + 42x = 5625x – 5y = 100 • 3y = 2x-4x + 6y = 3 • 7x + y = 1328x + 4y = -12 • 2x – 3y = -153y – 2x = 15 • 8y – 24x = 649y + 45x = 72 • 2x + 2y = -104x – 4y = -16

  9. Reflection • If no solution means there is no ordered pair that will make both equations true, what will that look like when graphed? • If infinitely many solutions means any ordered pair that makes one equation true will make the other equation true as well, what will that look like when graphed?

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