Presentation on theme: "Systems with No Solution or Infinitely Many Solutions"— Presentation transcript:
1Systems with No Solution or Infinitely Many Solutions September 15, 2014Pg. 21 in Notes
2Warm-Up (pg. 20)Solve the following system of equations using the elimination method.7x + 4y = 29x – 4y = 30Questions on Friday’s Assignment?
3No Solution/Infinitely Many Solutions Title: page 21
4Essential QuestionHow do you know if a system has one solution, no solution, or infinitely many solutions?
5Systems with One Solution Solution will be an ordered pair.
6Systems 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.
7Systems 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.
8Practice – 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
9ReflectionIf 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?