Bell Work (7 minutes)

Solving Linear Systems of Equations and Inequalities by Graphing Unit 7 Solving Linear Systems of Equations and Inequalities by Graphing

Bell Work Review (3 minutes) You found a system of equations to represent Desmond’s missing records situation. a. How is this system different from the systems of equations you solved in the last Exploring? b. Will this difference prevent you from using a table and/or a graph to solve the system? c. How do you know whether to use slope-intercept form or standard form for the equations in system of linear equations?

I Do (3 minutes) Sketch the graph of each equation: 𝒙+𝒚=𝟏𝟐 𝟏𝟓𝒙+𝟑𝟎𝒚=𝟐𝟒𝟎

We Do (5 minutes) What does this solution tell you about Desmond’s missing records problem regarding how many lots of each size were mowed during the week?   Suppose this time, Desmond charges $20 for the standard-sized interior lots and $25 for the larger corner lots. He received a total of $300 for mowing 14 lots during the past week. Using x to represent the number of interior lots mowed and y to represent the number of corner lots mowed, set up a system of two linear equations to model this situation.

You Do (7 minutes) The sum of two numbers is 186. The difference between the same numbers is 32. Create a system of equations to model the situation, and then solve the system using a graphical strategy.

Your Turn (HW) Dr. Alvarado is a chemist. She needs to mix 10 liters of a solution of a certain chemical that is 64% pure. (That is, 64% is the chemical, and the rest is water.) To do this, she will mix a solution that is 70% pure with one that is 50% pure. How many liters of each should she use? 1) Choose variables and identify what they will represent. 2) Write a system of equations that Dr. Alvarado can use to find her answers. 3) Use a table or graph to solve the system. 4) Show how to check your answer. Then write your answer in a sentence.