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8.1 Systems of Equations in Two Variables Day 1

8.1 Systems of Equations in Two Variables Day 1. Do Now Solve for y 1) X – y = 5 2) 2x + y = 1. System of Equations. There are three ways to solve a system of equations in two variables: Graphing Substitution Elimination. Solving by Graphing.

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8.1 Systems of Equations in Two Variables Day 1

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  1. 8.1 Systems of Equations in Two VariablesDay 1 Do Now Solve for y 1) X – y = 5 2) 2x + y = 1

  2. System of Equations • There are three ways to solve a system of equations in two variables: • Graphing • Substitution • Elimination

  3. Solving by Graphing • When graphing a system of equations, the solution is the intersection • 1 solution: 1 intersection • 0 solutions: parallel lines • Infinitely many solutions: lines are identical

  4. Ex • Solve by graphing

  5. Substitution Method • 1) Solve equation 1 for one variable • 2) Substitute equation 1 into equation 2 • 3) Solve for remaining variable • 4) Solve for 2nd variable

  6. Ex • Solve using substitution

  7. Elimination Method • 1) Multiply both equations by constants so that one pair of variables have the same coefficient • 2) Add or subtract equations to eliminate 1 variable • 3) Solve for the remaining variable • 4) Solve for the 2nd variable

  8. Ex • Solve using the elimination method

  9. Ex • Solve

  10. Ex • Solve

  11. Ex • Solve

  12. Closure • Solve • HW: p.688 #1-37 odds

  13. 8.1 Systems of Equations in Two VariablesDay 2 • Do Now • Solve

  14. HW Review: p.688 #1-37 odds

  15. Applications • When approaching a word problem, and there are 2 different measurements, you want to write one equation for each measurement

  16. Ex • At SnackMix.com, caramel corn worth $2.50 per pound is mixed with honey roasted mixed nuts worth $7.50 per pound in order to be 20 lbs of a mixture worth $4.50 per pound. How much of each snack is used?

  17. Ex • Kerry’s motorboat takes 3 hr to make a downstream trip with a 3mph current. The return trip against the same current takes 5 hr. Find the speed of the boat in still water

  18. Ex • The price and supply of a satellite radio are related by the equation y = 90 + 30x • The price and demand of the radio are related by the equation y = 200 – 25x • The equilibrium point for this product is when both are equal. Find the equilibrium point

  19. Closure • College students spend a total of $819 on textbooks and computer equipment. They spend $183 more on textbooks than on computer equipment. How much do they spend on each one? • HW: p.689 #41-61 odds

  20. 8.1 Systems of EquationsDay 3 • Do Now • Jackson Manufacturing offers its sales reps a choice between being paid a commission of 8% sales or being paid a monthly salary of $1500 plus a commission of 1% of sales. For what monthly sales do the two plans pay the same amount?

  21. HW Review: p.689 #41-61

  22. Closure • How do you solve a system of equations in 2 variables? Which method do you prefer? Why? • HW: none

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