Report

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 Terminology Graph Exactly One Infinite No Solution 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 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 3x – 4y = 14 Ex) 7x + 3y = -6 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? Method Graphing Substitution Elimination When to use it… 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 • 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 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