Presentation on theme: "Systems with No Solution or Infinitely Many Solutions"— Presentation transcript:
1 Systems with No Solution or Infinitely Many Solutions September 15, 2014Pg. 21 in Notes
2 Warm-Up (pg. 20)Solve the following system of equations using the elimination method.7x + 4y = 29x – 4y = 30Questions on Friday’s Assignment?
3 No Solution/Infinitely Many Solutions Title: page 21
4 Essential QuestionHow 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 + 16x – 2y = 5Let’s use substitution:6x – 2(3x + 1) = 56x – 6x – 2 = 5-2 = 5The 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 = -12Let’s use elimination:8x + 12y = 24-8x – 12y = -240 = 0Each 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.7x + y = 13 28x + 4y = -122x – 3y = -15 3y – 2x = 158y – 24x = 64 9y + 45x = 722x + 2y = -10 4x – 4y = -1624x – 27y = 42 -9y + 8x = 143/2 x + 9 = y 4y – 6x = 367y + 42x = 56 25x – 5y = 1003y = 2x -4x + 6y = 3
9 ReflectionIf 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?