1 / 16

Warm Up Solve each equation. 1. 2 x + 3 = 2 x + 4 2. 2( x + 1) = 2 x + 2

Warm Up Solve each equation. 1. 2 x + 3 = 2 x + 4 2. 2( x + 1) = 2 x + 2 3. Solve 2 y – 6 x = 10 for y. no solution. infinitely many solutions. y = 3 x + 5. Solve by using any method. y = 3 x + 2. x – y = 8. 5. 4. (6, –2). (1, 5). 2 x + y = 7. x + y = 4.

antwans
Download Presentation

Warm Up Solve each equation. 1. 2 x + 3 = 2 x + 4 2. 2( x + 1) = 2 x + 2

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Warm Up Solve each equation. 1.2x + 3 = 2x + 4 2. 2(x + 1) = 2x + 2 3. Solve 2y – 6x = 10 for y no solution infinitely many solutions y =3x + 5 Solve by using any method. y = 3x + 2 x – y = 8 5. 4. (6, –2) (1, 5) 2x + y = 7 x + y = 4

  2. Learning Targets Student will be able to: Solve special systems of linear equations in two variables. Classify systems of linear equations and determine the number of solutions.

  3. Systems with at least one solution are called consistent. A system that has no solution is an inconsistent system.

  4. Substitution y = x – 4 Solve . –x + y = 3 Inconsistent System.

  5. y = x – 4 Graph . –x + y = 3

  6. Substitution y =–2x + 5 Solve . 2x + y =1 Inconsistent System.

  7. y =–2x + 5 Graph . 2x + y =1

  8. If two linear equations in a system have the same graph, the graphs are coincident lines, or the same line. There are infinitely many solutions of the system because every point on the line represents a solution of both equations.

  9. y =3x + 2 Solve for y Solve . 3x – y +2= 0 Coincident Lines. There are infinitely many solutions.

  10. Solve for y y = x – 3 Solve . x – y –3 = 0 Coincident Lines. There are infinitely many solutions.

  11. Consistent systems can either be independent or dependent. An independent system has exactly one solution. The graph of an independent system consists of two intersecting lines. A dependent system has infinitely many solutions. The graph of a dependent system consists of two coincident lines.

  12. Classify the system. Give the number of solutions. 3y = x + 3 Solve x + y = 1 Solve for y The system is consistent and dependent. It has infinitely many solutions.

  13. Classify the system. Give the number of solutions. Solve for y x + y = 5 Solve 4+ y = –x The system is inconsistent. It has no solutions.

  14. Classify the system. Give the number of solutions. Distribute; Solve for y y = 4(x + 1) Solve y – 3 = x The system is consistent and independent. It has one solution.

  15. y = 20x + 100 y = 30x+ 80 y = 20x + 100 y = 30x+ 80 Matt has $100 in a checking account and deposits $20 per month. Ben has $80 in a checking account and deposits $30 per month. Will the accounts ever have the same balance? Explain. The accounts will have the same balance. The graphs of the two equations have different slopes so they intersect.

More Related