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Unit 1

Unit 1. Solving system of equations. System of equations. Define : system of equations - a set of two or more equations Define : solution of a system - ordered pair(s) that make all the equations true. Key concept : the solution to a system is where the graphs intersect. Lines are Parallel

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Unit 1

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  1. Unit 1 Solving system of equations

  2. System of equations Define: system of equations- a set of two or more equations Define: solution of a system- ordered pair(s) that make all the equations true. Key concept: the solution to a system is where the graphs intersect. Lines are Parallel No solution Lines coincide Infinitely many solutions Lines intersect 1 solution

  3. Solve by graphing • Solve by graphing: • Graph in y= • 2nd ,trace, intersection, enter, enter, enter

  4. System word problem Mr. Smith bought 2 lbs of jelly and 3 lbs of peanut butter. He paid $26.35. Mrs. Sing paid $18.35 for 1.5 lbs of jelly and 2 lbs of peanut butter. What was the price per pound of each item? 1st write two equations that model the above situation. ~Mr. Smith’s shopping trip ~Mrs. Sing’s shopping trip Then solve the system by graphing. (use CALC)

  5. System of inequalities The solution to a system of inequalities is not where the graphs intersect but where the shaded region overlap! Your answer is the your graph and shaded region

  6. System of inequalities Solve each system of inequalities

  7. System of inequalities

  8. System of inequality word problem Kayla wants to buy Hotdogs, hamburgers, or some of each for weekend meals. The Hotdogs costs $4 per pound and the Hamburger costs $3 per pound. She will spend at least $11 but no more than $15. a. Write a system of inequalities to model the situation. b. Graph the system to show the possible amounts Kayla could buy. Answer 4x + 3y ≥ 11 4x + 3y ≤ 15 x ≥ 0 y ≥ 0

  9. Solve a system by matrices There are other ways to solve a system besides graphing. One alternative way is using matrices. Matrices can be used to solve 2x2 systems and bigger. SOLVE the 3x3 system [2nd] , [matrix],  edit, type in systems, [2nd], [quit] [2nd] , [matrix],  MATH, rref, [A] The last column is your answer

  10. More Practice with Equations Textbook p. 138 #1- 8) The system has one solution since the lines intersect at (2, 1).

  11. Equations (Con’t) 11) 2nd equation: y = x + 6 There are no solutions, since the lines have the same slope.

  12. Graphing Inequalities P. 153 # 11 The solutions for a systems of inequalities are located where the shaded regions overlap.

  13. Systems (Con’t) 24)

  14. Why do we have to…. …learn this? I’m never going to use it. Job Du Jour Social Media Manager @ Elon University (NC) Summary: Full Time--The interactive media developer is a member of the University Communications staff and creates content for the university’s social media platforms and websites, managing the university’s presence and relationships with online constituencies in an evolving new media environment. Oversee and actively manage content and conversations on Elon’s Facebook, YouTube, Twitter, Linked-in, Flickr, Pinterest, Instagram and Livestream accounts. Produce a daily stream of information, spot photos and videos about important events and daily life on campus for posting to Elon’s social media platforms.

  15. Requirements Education: Bachelor's degree from four-year college or university; prefer majors in communications or marketing. Extensive experience developing and implementing strategies to use social media to effectively communicate with audiences. Skills: Level 3 - Ability to calculate figures and amounts such as proportions, percentages, area, circumference, and volume. Ability to apply concepts of basic algebra and geometry. Can you solve for r?

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