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Algebra I

Algebra I. Chapter 6 Notes. Section 6-1: Graphing Systems of linear equations, Day 1. What is a system of linear equations? Consistent – Inconsistent – Independent – Dependent –. Section 6-1: Graphing Systems of linear equations, Day 1. What is a system of linear equations?

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Algebra I

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  1. Algebra I Chapter 6 Notes

  2. Section 6-1: Graphing Systems of linear equations, Day 1 What is a system of linear equations? Consistent – Inconsistent – Independent – Dependent –

  3. Section 6-1: Graphing Systems of linear equations, Day 1 What is a system of linear equations? Two equations with two variables. Consistent – a system with at least one solution Inconsistent – a system with no solutions Independent – a system with exactly one solution Dependent – a system with an infinite number of solutions

  4. Section 6-1: Graphing Systems, Day 1

  5. Section 6-1: Graphing Systems, Day 1 Steps for solving systems by graphing Graph the system (Use a Ruler!) y = -3x + 10 y = x – 2 1. Graph the first equation on the graph 2. Graph the second equation on the graph 3. Find where the lines intersect 4. CHECK your answer

  6. Section 6-1: Graphing Systems, Day 1 Solve the following systems by graphing Ex) y = ½ x Ex) 8x – 4y = 16 y = x + 2 -5x – 5y = 5

  7. Section 6-1 Graphing Systems, Day 2 Systems that have no solutions – Systems that have an infinite number of solutions -

  8. Section 6-1 Graphing Systems, Day 2 Systems that have no solutions – Lines that are parallel and therefore never intersect Systems that have an infinite number of solutions – Equations that end up graphing the same line

  9. Section 6-1 Graphing Systems, Day 2 Solve the following systems by graphing Ex) 2x – y = -1 Ex) y = -2x - 3 4x – 2y = 6 6x + 3y = -9

  10. Section 6-1 Graphing Systems, Day 2 Use the graph to determine whether each system is consistent or inconsistent, independent or dependent. Ex) y = -2x + 3 y = x – 5 Ex) y = -2x – 5 y = -2x + 3

  11. Section 6-2: Solving Systems by Substitution, Day 1 Steps for solving using substitution: 1) Solve ONE equation for ONE variable (Choose the a variable with a coefficient of 1 or -1 to make it easy) 2) Substitute the expression from step 1 into the OTHER equation for the variable 3) Solve the new equation 4) Plug in the solution from step 3 into either equation to find the other variable 5) Check your answer! Ex) y = 2x + 1 3x + y = -9

  12. Section 6-2: Solving Systems by Substitution, Day 1 Solve the systems using substitution Ex) y = x + 5 Ex) x + 2y = 6 3x + y = 25 3x – 4y = 28

  13. Section 6-2: Solving Systems by Substitution, Day 2 Special Case Solutions Solve the systems using substitution Ex) y = 2x – 4 Ex) 2x – y = 8 -6x + 3y = -12 -2x + y = -3

  14. Section 6-3: Solving systems using the elimination method (add/sub) Steps for solving using the elimination method 1) Write the system so like terms are aligned 2) Add or subtract the equations, elimination a variable and solve 3) Plug in the solution from step 2 to find the other variable 4) Check your answer! Ex) 4x + 6y = 32 3x – 6y = 3

  15. Section 6-3: Solving systems using the elimination method (add/sub) Solve using elimination Ex) 4y + 3x = 22 Ex) 7x + 3y = -6 3x – 4y = 14 7x – 2y = -31

  16. Section 6-4: Elimination with Multiplication, Day 1 Steps for solving using the elimination method 1) Write the system so like terms are aligned 2) Multiply one or both equations by a number, or 2 different numbers to get like coefficients for one variable 3) Add or subtract the equations, elimination a variable and solve 4) Plug in the solution from step 2 to find the other variable 5) Check your answer! Ex) 5x + 6y = -8 2x + 3y = -5

  17. Section 6-4: Elimination with Multiplication, Day 1 Solve using the elimination method Ex) 4x + 2y = 8 Ex) 6x + 2y = 2 3x + 3y = 9 4x + 3y = 8

  18. Section 6-4: Solve using elimination, Day 2 Solve using elimination. Be careful of special cases. Ex) 3x + y = 5 Ex) x + 2y = 6 6x = 10-2y 3x + 6y = 8

  19. Section 6-4: Solve using elimination, Day 2 Solve the following systems using elimination Ex) 8x + 3y = 4 Ex) 12x – 3y = -3 Ex) 8x + 3y = -7 -7x + 5y = -34 6x + y = 1 7x + 2y = -3

  20. Section 6-5: Which method is best?

  21. Section 6-5: Best Method Determine which method is best, then solve the system using that method Ex) 2x + 3y = -11 Ex) 3x + 4y = 11 -8x – 5y = 9 y = -2x - 1

  22. Section 6-5: Word Problems Ex) Jenny has $24 to spend on tickets at the carnival. The small rides cost $2 per ticket, and the large rides cost $3 per ticket. She buys a total of 7 tickets. How many small ride tickets did she buy? How many large ride tickets did she buy? Write and solve a system. Ex) Martha has a total of 40 DVDs of movies and TV shows. The number of movies is 4 less than 3 times the number of TV shows. Write and solve a system to find the numbers of movies and TV shows she owned.

  23. Section 6-6: Systems of Linear Inequalities Steps for Solving Systems of Linear Inequalities 1) Graph the first equation • Choose the correct line (Solid or dashed) • Shade the correct side 2) Graph the second equation • Choose the correct line (Solid or dashed) • Shade the correct side 3) Darken the shaded areas that overlap Ex) y > -2x + 1 y < x + 3

  24. Section 6-6: Systems of Linear Inequalities Solve the following S.o.L.E by graphing Ex) x > 4 Ex) y > -2 y < x – 3 y < x + 9

  25. Section 6-6: Graphing systems of linear inequalities Solve the following S.o.L.E by graphing Ex) 3x – y > 2 Ex) y > 3 3x – y < -5 y < 1

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