Daily Learning Plan: Algebra I Part 2 Unit 6: Systems of Equations and Inequalities Day: Date: Topic: ENDURING UNDERSTANDINGS: 1. Recognizing and analyzing simultaneous relationships between two variables is essential to predict outcomes and make decisions. 2. When you need to find two unknown values, you may be able to write and solve a system of linear equations. 3. There are several ways to solve linear systems of equations and inequalities and the number of solutions depends on the type of system. ESSENTIAL QUESTIONS: 1. Recognizing and analyzing simultaneous relationships between two variables is essential to predict outcomes and make decisions. 2. When you need to find two unknown values, you may be able to write and solve a system of linear equations. 3. There are several ways to solve linear systems of equations and inequalities and the number of solutions depends on the type of system. SOL OBJECTIVES (2009): A.4 The student will solve multistep linear and quadratic equations in two variables, including e) solving systems of two linear equations in two variables algebraically and graphically; and f) solving real-world problems involving equations and systems of equations. A.5 The student will solve multistep linear inequalities in two variables, including a) solving multi-step linear inequalities algebraically and graphically; b) justifying steps used in solving inequalities, using axioms of inequalities and properties of order that are valid for the set of real numbers and its subsets; c) solving real-world problems involving inequalities; d) solving systems of inequalities. A.6 The student will graph linear equations and linear inequalities in two variables, including a) determining the slope of a line when given an equation of the line, the graph of the line, or two points on the line. Slope will be described as rate of change and will be positive, negative, zero, or undefined; and b) writing the equation of a line when given the graph of the line, two points on the line, or the slope and a point on the line. OBJECTIVES/COMPETENCIES: A1P2.EQ.6.1 The student will solve systems of equations in two variables algebraically and graphically, using graphing calculators to verify solutions. (SOL A.4 e) A1P2.EQ.6.2 The student will solve linear inequalities and systems of linear inequalities in two variables and use a graph to represent the solution set. (SOL A.5 d). MATERIALS: 5 in 10, Notes, Exit Ticket, Homework HOOK / WARM-UP: 5 in 10 Graphing to Solve Systems INSTRUCTIONAL STRATEGIES & PROCEDURES: Notes Solving Linear Systems by Substitution Notes 5-9 (popcorn) have students come up to smartboard and do one step Application Try these with a partner CLOSURE: Exit Ticket HOMEWORK: Solving Linear Systems by Substitution LESSON EVALUATION:
Name Date Block Pledge 3. Graph and check to solve the linear system. 2x - y = 3 x + 2y = 4 Five in Ten (Graphing to Solve Systems) 1. Decide whether (3, 5) is a solution of the linear system. 2x 5y = -31-3x + y = 14 4. Graph and check to solve the linear system. x = -1-4x + y = 2 2. Graph and check to solve the linear system. y = x + 3 y = -3x - 1 5. The Smith family made an $800 downpayment and pays 475 a month for new furniture. At the same time, the Cooper family made a $500 downpayment and pays $95 a month for their furniture. How many months does will it take before the amounts they paid are equal? Write a system of equations for this system. Just write the equations; don t solve!
Name Date Block Note-taker: Solving Linear Systems by Substitution SOLVING A LINEAR SYSTEM BY SUBSTITUTION: 1. Solve one of the equations for one of its variables. 2. Substitute the expression from step 1 into the other equation, and solve for the other variable. 3. Substitute the value from step 2 into the revised equation from step 1 and solve. 4. Check the solution in each of the original equations. Solve the linear system. 1. y = 2x 2x + 5y = -12 2. 2y = -3x 4x + y = 5 3. 3x + y = 0 x y = 4 4. 3x - y = 9 2x + y = 6
5. 3x + y = 5 2x y = 10 6. -x + y = 1 2x + y = -2 7. 2x + 6y = 15 x = 2y 8. 2x + 2y = 3 x - 4y = -1 9. 2x - 5y = -13 x + 3y = -1 Summary:
(continued) Note-taker: Solving Linear Systems by Substitution Example 3: Writing & Using Linear System 1. An office supply company sells two types of fax machines. They charge $150 for one of the machines and $225 for the other. If the company sold 22 fax machines for a total of $3,900 last month, how many of each type were sold? Try these with a partner. 1. A quilt maker sews both large and small quilts. A large quilt requires 8 yards of fabric while a small quilt requires 3 yards. How many of each size quilt did she make if she used a total of 90 yards of fabric to make 15 quilts? 2. y = x - 1 x - 5y = -15 3. x + 2y = 4 -x + y = -7
Name Date Block Score EXIT TICKET: Solving Linear Systems by Graphing or Substitution 1. Solve by graphing: y = x + 1-2x + y = -1 2. Solve by substitution: y = 2x + 7 4x + 3y = 31 Name Date Block Score EXIT TICKET: Solving Linear Systems by Graphing or Substitution 1. Solve by graphing: y = x + 1-2x + y = -1 2. Solve by substitution: y = 2x + 7 4x + 3y = 31
Name Date Block Score Use substitution to solve the linear system. HW: Solving Linear Systems by Substitution 1. 3x + y = 5 2. y = 5 -x + y = -7 2x + y = -9 3. x = y + 3 4. y = -2x + 1 x + y = 5 -x - y = -5 5. y = x 5 6. 2x y = -2 2x - 3y = 7 4x + y = 20 7. 2x + 5y = 7 8. 2x = 8 x - y = -7 x + y = 2
Graph and check to solve the linear system. 9. y = x + 1 10. y = x + 3 y = -2x + 4 3x + y = -1 11. x = -2 12. y = 4 2x + y = 1 1 y x 2 2