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? 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

Section 6-1: Graphing Systems, Day 1 Number of Solutions Exactly One Infinite No Solution Terminology Graph

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 3. Find where the lines intersect 4. CHECK your answer

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Section 6-5: Which method is best? When to use it… Graphing Substitution Elimination

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

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.

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 3) Darken the shaded areas that overlap Ex) y > -2x + 1 y < x + 3

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

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