Presentation on theme: "Lesson 3-2 Example 1 Use substitution to solve the system of equations. x + 4y = 26 x – 5y = –10 Solve by Using Substitution x + 4y =26First equation x."— Presentation transcript:
Lesson 3-2 Example 1 Use substitution to solve the system of equations. x + 4y = 26 x – 5y = –10 Solve by Using Substitution x + 4y =26First equation x =26 – 4ySubtract 4y from each side. Solve the first equation for x in terms of y.
Lesson 3-2 Example 1 Substitute 26 – 4y for x in the second equation and solve for y. Solve by Using Substitution x – 5y =–10Second equation 26 – 4y – 5y =–10Substitute 26 – 4y for x. –9y=–36Subtract 26 from each side. y=4Divide each side by –9.
Lesson 3-2 Example 1 Now substitute the value for y in either of the original equations and solve for x. Solve by Using Substitution Answer: The solution of the system is (10, 4). x + 4y=26First equation x + 4(4)=26Replace y with 4. x + 16=26Simplify. x=10Subtract 16 from each side.
Lesson 3-2 CYP 1 A. A B. B C. C D. D Solve the system of equations using substitution. What is the solution to the system of equations? x – 3y = 2 x + 7y = 12 A.(1, 5) B. C.(8, 2) D.(5, 1)
Lesson 3-2 Example 2 Lancaster Woodworkers Furniture Store builds two types of wooden outdoor chairs. A rocking chair sells for $265 and an Adirondack chair with footstool sells for $320. The books show that last month, the business earned $13,930 for the 48 outdoor chairs sold. How many of each chair were sold? Read the Test Item Solve by Substitution You are asked to find the number of each type of chair sold.
Lesson 3-2 Example 2 Step 1 Define variables and write the system of equations. Let x represent the number of rocking chairs sold and y represent the number of Adirondack chairs sold. Solve by Substitution x + y =48The total number of chairs sold was x + 320y =13,930The total amount earned was $13,930. Solve the Test Item
Lesson 3-2 Example 2 Step 2 Solve one of the equations for one of the variables in terms of the other. Since the coefficient of x is 1, solve the first equation for x in terms of y. Solve by Substitution x + y =48First equation x=48 – ySubtract y from each side.
Lesson 3-2 Example 2 Step 3 Substitute 48 – y for x in the second equation. Solve by Substitution 265x + 320y =13,930Second equation 265(48 – y) + 320y =13,930Substitute 48 – y for x. 12,720 – 265y + 320y=13,930Distributive Property 55y=1210Simplify. y=22Divide each side by 55.
Lesson 3-2 Example 2 Step 4 Now find the value of x. Substitute the value for y into either equation. Solve by Substitution x + y =48First equation x + 22 =48Replace y with 22. x=26Subtract 22 from each side. Answer:They sold 26 rocking chairs and 22 Adirondack chairs.
Lesson 3-2 CYP 2 A. A B. B C. C D. D A.210 adult; 120 children B.120 adult; 210 children C.300 children; 30 adult D.300 children; 30 adult AMUSEMENT PARKS At Amys Amusement Park, tickets sell for $24.50 for adults and $16.50 for children. On Sunday, the amusement park made $6405 from selling 330 tickets. How many of each kind of ticket was sold?