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SHOPPING (Systems of Linear Equations – Standard Form) Student Worksheet: A clothing store sells jeans for one price and tee shirts for another price. Sam purchases two pair of jeans and six tee shirts for $60. Jose purchases four pairs of jeans and three tee shirts for $75. 1. Write a system of equations that could be used to determine the cost of one pair of jeans (x) and the cost of one tee shirt (y). 2. Solve each equation for y. Enter the equations into your calculator. 3. Set up an appropriate graphing window, and then graph the equations. 4. Use your calculator to find the point of intersection of the two lines. 5. What is the meaning of this point of intersection in the context of this problem? Use mathematics to justify your answer. 6. How much does each pair of jeans cost? Use mathematics to explain how you determined your answer. Use words, symbols, or both in your explanation. 7. How much does each tee shirt cost? Use mathematics to explain how you determined your answer. Use words, symbols, or both in your explanation. Lesson Plan: Systems of Linear Equations – Standard Form Page 1 SHOPPING (Systems of Linear Equations – Standard Form) Answer Key 1. Write a system of equations that could be used to determine the cost of one pair of jeans (x) and the cost of one tee shirt (y). 2x + 6y = 60 4x + 3y = 75 2. Solve each equation for y. Enter the equations into your calculator. Y = (-1/3)x +10 Y = (-4/3)x +25 3. Set up an appropriate graphing window, and then graph the equations. 4. Use your calculator to find the point of intersection of the two lines. (15, 5) 5. What is the meaning of this point of intersection in the context of this problem? Use mathematics to justify your answer. The x value of the point of intersection is the cost of a pair of jeans and the y value is the cost of a tee shirt. This is true because the point of intersection of two lines is the point that makes both equations true. 6. How much does each pair of jeans cost? Use mathematics to explain how you determined your answer. Use words, symbols, or both in your explanation. A pair of jeans cost $15. Example explanation: I found this by determining the x value of the point of intersection. 7. How much does each tee shirt cost? Use mathematics to explain how you determined your answer. Use words, symbols, or both in your explanation. A tee shirt cost $5. Example explanation: (algebraic) 2x + 6y = 60 4x + 3y = 75 -4x –12y = -120 4x + 3y = 75 ___________ -9y = -45 y = 5 tee shirts cost $5 Lesson Plan: Systems of Linear Equations – Standard Form Page 2