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Main Idea and New Vocabulary NGSSS Example 1: Solve a System by Substitution Example 2: Real-World Example Example 3: Real-World Example Five-Minute Check • Solve systems of equations by substitution. • substitution MA.8.A.1.3 Use tables, graphs, and models to represent, analyze, and solve real-world problems related to systems of linear equations. Solve a System by Substitution Solve the system of equations by substitution. y = x + 15 y = 4x Since y is equal to 4x, you can replace y with 4x in the first equation. y= x + 15 Write the equation. 4x = x + 15 Replace y with 4x. –x –x 3x = 15 Subtract x from each side. Simplify. Solve a System by Substitution 3 3 x =5 Divide each side by 3. Simplify. Since x = 5 and y = 4x, then y = 20 when x = 5. The solution of this system of equations is (5, 20). Check the solution by graphing. Answer: (5, 20) Solve the system of equations by substitution. y=x–7 y = 2x A. (–7, –14) B. (0, –7) C. (7, 0) D. (7, 14) SALES A store sold 84 black and gray T-shirts one weekend. They sold 5 times as many black T-shirts as gray T-shirts. Write a system of equations to represent this situation. Draw a bar diagram. Then write the system. Let x represent the number of black T-shirts and y represent the number of gray T-shirts. x + y = 84 The total number of black and gray T-shirts is 84. x = 5y There were 5 times as many black T-shirts as gray T-shirts. Answer: The system of equations is x + y = 84 and x = 5y. FAIR Devin and Emily spent a total of $24 at the fair. Devin spent three times as much as Emily spent. Let x represent the amount Emily spent and let y represent the amount Devin spent. Write a system of equations to represent this situation. A. x − y = 24 x = 3y B. 3x + y = 24 y = 3x C. x + y = 24 y = 3x D. x + y = 24 x = 3y SALES A store sold 84 black and gray T-shirts one weekend. They sold 5 times as many black T-shirts as gray T-shirts. Solve the system by substitution. Interpret the solution. The system of equations is x + y = 84 and x = 5y. Since x is equal to 5y, you can replace x with 5y. x + y = 84 Write the equation. 5y + y = 84 Replace x with 5y. 6y = 84 Simplify. Divide each side by 6. y = 14 Simplify. Since y = 14 and x = 5y, then x = 70 when y = 14. Answer: The solution is (70, 14). This means that the store sold 70 black and 14 gray T-shirts. Check Check the solution by graphing. The graphs of the functions intersect at the point (70, 14). FAIR Devin and Emily spent a total of $24 at the fair. Devin spent three times as much as Emily spent. Let x represent the amount Emily spent and let y represent the amount Devin spent. Solve the system by substitution. Interpret the solution. A. (18, 6); Emily spent $18 and Devin spent $6. B. (6, 18); Emily spent $6 and Devin spent $18. C. (15, 5); Emily spent $15 and Devin spent $5. D. (5, 15); Emily spent $5 and Devin spent $15. Solve the system of equations by substitution. y = 2x + 3 y = 12 A. (4.5, 12) B. (7.5, 12) C. (12, 4.5) D. (12, 27) Solve the system of equations by substitution. y=x–6 y=3 A. (–3, 3) B. (2, 3) C. (3, 9) D. (9, 3) Solve the system of equations by substitution. y=x–4 y= x A. (–6, –10) C. (6, 2) B. (–3, –1) D. (12, 8) Solve the system of equations by substitution. y = –4x – 8 y = –2x A. (−8, 16) B. (−4, −8) C. (−4, 8) D. (2, –4) Together, Wally and Sam have 20 toy trains. Wally has 8 more trains than Sam. How many trains does each boy have? A. Sam has 14 trains and Wally has 6 trains. B. Sam has 6 trains and Wally has 14 trains. C. Sam has 8 trains and Wally has 12 trains. D. Sam has 10 trains and Wally has 28 trains.