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

Solve systems of equations by substitution. Main Idea/Vocabulary

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

Solve a System by Substitution 3 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

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

Draw a bar diagram. Then write the system. 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

x + y = 84 The total number of black and gray T-shirts is 84. 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. Example 2

FAIR Devin and Emily spent a total of $24 at the fair 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 Example 2 CYP

x + y = 84 Write the equation. 5y + y = 84 Replace x with 5y. 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. Example 3

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).  Example 3

A. (18, 6); Emily spent $18 and Devin spent $6. 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