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Warm ups

Warm ups. What is the slope and y intercept ?. 8.1 Graphing Systems of Equations. Objective: To solve systems of equations by graphing. System of Linear Equations:. System of Linear Equations: Two or more linear equations.

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Warm ups

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  1. Warm ups • What is the slope and y intercept?

  2. 8.1 Graphing Systems of Equations Objective: To solve systems of equations by graphing.

  3. System of Linear Equations: System of Linear Equations:Two or more linear equations. • A solution to the system of linear equations is any ordered pair that makes BOTH equations true.

  4. Three Types of Solutions: Intersection is Solution Infinite Solutions One Solution No Solution Same slope Same y-intercept “Same line  Intersect infinitely” Different slope Different y-intercept “Intersect at one point” Same slope Different y-intercept “Run parallel  Never intersect”

  5. Examples: Solve each system by graphing. 1) y = –x + 1 y = 2x + 4 y = –x + 1 Slope: -1 Y-int: (0, 1) y = 2x + 4 Slope: 2 Y-int: (0, 4) Different slope Different y-intercept “Intersect at one point” The solution of the system is: (-1, 2) x = –1, y = 2

  6. 2) x + y = 1 y = –x + 3 x + y = 1 –x –x y = - x + 1 Slope: -1 Y-int: (0, 1) y = –x + 3 Slope: –1 Y-int: (0, 3) Same slope Different y-intercept “Run parallel  Never intersect” The solution of the system is: no solution

  7. 3) x – 2y = 4 2x – 4y = 8 x – 2y = 4 –x –x –2y = –x + 4 –2 –2 –2 y = ½ x – 2 Slope: ½ Y-int: (0, –2) 2x – 4y = 8 –2x –2x –4y = –2x + 8 –4 –4 –4 Y = ½ x – 2 Slope: ½ Y-int: (0, –2) The solution of the system is: infinite solutions Same slope Same y-intercept “Same line  Intersect infinitely”

  8. Try with a Partner: 4) y = 3x – 3 x + y = 1 y = 3x – 3 Slope: 3 Y-int: (0, –3 ) x + y = 1 –x –x y = –x + 1 Slope: –1 Y-int: (0, 1) Different slope Different y-intercept “Intersect at one point” The solution of the system is: (1, 0) x = 1, y = 0

  9. Summarize:HOW MANY ANSWERS?

  10. TRY ON OWN Answer the four multiple choice questions on the elmo.

  11. Speaker and Scribe Review

  12. Review

  13. Review

  14. Write in STANDARD

  15. Determine Value of r.

  16. Homework 8.1 Graphing Systems of Linear Equations (2 sides)

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