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Teacher Page Algebra/ Day 2 Systems of Equations 9-12.A.3.1 9-12.A.3.4 9-12.A.3.5 (90 min) Model real-world phenomena using linear equations and linear inequalities interpret resulting solutions, and use estimation to detect errors. Solve systems of linear equations in two variables algebraically and graphically Solve applications involving systems of two equations in two variables. 9-12.A.3.8 Determine whether the graphs of two given linear equations are parallel, perpendicular, coincide or none of these. 1 The Fun Guys game rental store charges an annual fee of $5 plus $5.50 per game rented. The Game Bank charges an annual fee of $17 plus $2.50 per game. For how many game rentals will the cost be the same at both stores? What is that cost? A 3 games; $22 C 4 games; $27 B 2 games; $16 D 6 games; $38 by using substitution. Express your answer as an ordered pair. 2 Solve A ( 3, −2) C B (− 3 , –3) D 8 (− 3 , 1) 4 (−2, 3) 3 Big Dog Snowboard Co. charges $15 for equipment rental plus $35 per hour for snowboarding lessons. Half-Pipe Snowboards, Inc. charges $40 for equipment rental plus $25 per hour for lessons. Write an equation for the cost of equipment rental and lessons at each company. For what number of hours is the cost of equipment and lessons the same for each company? In the answer box provided, with words, graphs, tables or equations, show your solution to the problem. Only work within the answer box will be scored. 3) Teacher Page Algebra/ Day 2 Systems of Equations (90 min) 4 A zookeeper needs to mix a solution for baby penguins so it has the right amount of medicine. Solution A has 20% medicine. Solution B has 4% medicine. How many ounces of each solution are needed to obtain 10 ounces of 8% medicine? a. Write an equation for the volume of solution b. Write an equation based on the amount of medicine. c. Solve the system to find how many ounces of each solution are needed to obtain 10 ounces of 8% medicine. In the answer box provided, with words, graphs, tables or equations, show your solution to the problem. Only work within the answer box will be scored. 4) Teacher Page Algebra/ Day 2 Systems of Equations Answer page (90 min) Answer Page 1 ANS: C Write a system of equations. Fun Guys Game Bank Total cost y y is = = cost 5.5 2.5 per game plus + + annual fee 5 17 Graph the two equations. 100 y 90 80 70 60 50 40 30 20 10 3 6 9 12 15 18 21 x The lines appear to intersect at (4, 27). So the cost will be the same after 4 games, and that cost will be $27. A B C D Feedback Write and solve a system of equations. Each equation should represent the total cost at a store. Check that you used inverse operations correctly when solving. Correct! Write and solve a system of equations. Each equation should represent the total cost at a store. Teacher Page Algebra/ Day 2 Systems of Equations Answer page 2 ANS: D Step 1 (90 min) The second equation is solved for y. Step 2 Substitute for y in the first equation. Simplify and solve for x. Step 3 Divide both sides by 4. x = −2 Step 4 y = −2 3 (−2, 3) A B C D Write one of the original equations. Substitute −2 for x. Find the value of y. Write the solution as an ordered pair. Feedback You reversed the order of the values. Include the variable x when substituting x + c for y. When combining like terms, remember that x means 1x. Correct! 3 a). Big Dog Snowboard Co: C(h) = 35h + 15 ; Half-Pipe Snowboards, Inc: C(h) = 25h + 40 b). 2.5 hours 4 Begin by writing an equation for the volume needed and an equation for the amount of medicine needed. Let a = volume of solution A. Let b = volume of solution B. or a). The equation for the volume of solution: b). the equation for the amount of medicine: c). 2.5 ounces of A and 7.5 ounces of B Solve the system by substituting the first equation into the second. Substitute for a. Distribute. Simplify. Substitute b in the original equation. The mixture will contain 2.5 ounces of solution A and 7.5 ounces of solution B.