Systems with Quadratic Equations 3/17/2011 ©Evergreen Public Schools 2010

2-7 Solving Equations With Algebra Tiles powerpoint Learning Target Target 10 Level 3 I can solve problems with systems of equations and inequalities. Equations can be linear, exponential or quadratic. What do you know about systems of equations? M2.1.B Solve problems that can be represented by systems of equations and inequalities. ©Evergreen Public Schools 2010

©Evergreen Public Schools 2010 Launch In a system of two linear equations, how many solutions are possible? Convince yourself. Convince a friend. Convince a skeptic. 0 or 1 or infinite ©Evergreen Public Schools 2010

©Evergreen Public Schools 2010 Launch In a system with a linear equation and a quadratic equation, how many solutions are possible? Convince yourself. Convince a friend. Convince a skeptic. 0, 1 or 2 4 ©Evergreen Public Schools 2010

©Evergreen Public Schools 2010 Launch List the different methods do you know for solving a system of equations. Algebra – substitution, addition, elimination Graph Table With graph calc You may want to post these to make them public for the exploration 5 ©Evergreen Public Schools 2010

©Evergreen Public Schools 2010 Explore ©Evergreen Public Schools 2010

System of Equations Use 2 methods to solve 5y – x = – 20 y = x – 8 You and your partner must each choose a different method. answer: x = 5, y = -3 Montior: Look for different methods. Find a graphing method. This is what we will use to solve exponential functions. Compare your answers. Make any edits you want. 7 ©Evergreen Public Schools 2010

System of Equations Use 2 methods to solve y = x2 – x – 6 y = 2x – 2 You and your partner must each choose a different method. answer: (4, 6) and (-1, -4) Montior: Look for different methods. Have a student who solved it algebraically show their work. Compare your answers. Make any edits you want. 8 ©Evergreen Public Schools 2010

©Evergreen Public Schools 2010 System of Equations Jason is traveling on a highway at a constant rate of 50 miles per hour but has a 10 mile head start from his friend Alan.  To catch up to the Jason's passing car, Alan accelerates at a constant rate.  The distance d, in miles, that Alan's car travels as a function of time t, in hours, since Jason's car has passed is given by d = 360t2. Write and solve a system of equations to calculate how long it takes Alan's car to catch up with Jason's car. 60t = 360t2 3600t2 -60t = 0 60t2 -1t = 0 t(60t-1) = 0 t = 0 or t o 1/60 hour t = 1 minute 9 ©Evergreen Public Schools 2010

©Evergreen Public Schools 2010 Team Practice ©Evergreen Public Schools 2010

©Evergreen Public Schools 2010 Debrief Consider solving a system with two linear equations similar to solving a system with one linear and one quadratic equations How are they similar? How are they different? ©Evergreen Public Schools 2010

©Evergreen Public Schools 2010 2-7 Solving Equations With Algebra Tiles powerpoint Learning Target 5 3 1 2 4 Did you hit the target? Target 10 Level 3 I can solve problems with systems of equations and inequalities. Equations can be linear, exponential or quadratic. Rate your understanding of the target from 1 to 5. ©Evergreen Public Schools 2010

©Evergreen Public Schools 2010 Practice Practice 9.3A ©Evergreen Public Schools 2010