# Systems with No Solution or Infinitely Many Solutions

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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
Title: page 21

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

Systems with One Solution
Solution will be an ordered pair.

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.

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.

Practice – Determine whether each of the following systems of equations has one solution, no solution, or infinitely many solutions. 7x + y = 13 28x + 4y = -12 2x – 3y = -15 3y – 2x = 15 8y – 24x = 64 9y + 45x = 72 2x + 2y = -10 4x – 4y = -16 24x – 27y = 42 -9y + 8x = 14 3/2 x + 9 = y 4y – 6x = 36 7y + 42x = 56 25x – 5y = 100 3y = 2x -4x + 6y = 3

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?