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Lesson Menu. Main Idea and New Vocabulary Example 1: Solve a System by Substitution Example 2: Real-World Example Example 3: Real-World Example. Solve systems of equations by substitution. substitution. Main Idea/Vocabulary. Solve a System by Substitution.

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  1. Lesson Menu Main Idea and New Vocabulary Example 1: Solve a System by Substitution Example 2: Real-World Example Example 3: Real-World Example

  2. Solve systems of equations by substitution. • substitution Main Idea/Vocabulary

  3. 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 Subtract x from each side. 3x = 15 Simplify. Example 1

  4. 3 3 Solve a System by Substitution Divide each side by 3. x = 5 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) Example 1

  5. Solve the system of equations by substitution. y = x – 7y = 2x A. (–7, –14) B. (0, –7) C. (7, 0) D. (7, 14) Example 1 CYP

  6. 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. Example 2

  7. Let x represent the number of black T-shirts and y representthe 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. Example 2

  8. 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 = 24x = 3y B.3x + y = 24y = 3x C.x + y = 24y = 3x D.x + y = 24x = 3y Example 2 CYP

  9. Divide each side by 6. 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. y = 14 Simplify. Example 3

  10. 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. CheckCheck the solution by graphing. The graphs of the functions intersect at the point (70, 14).  Example 3

  11. 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. Example 3 CYP

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