1. 1.4 Solving Systems of Equations

3. Example 1 1. Choose an equation and solve for a variable. 2. Substitute into the other equation 3. Solve for the variable 4. Substitute into either equation and solve for the second variable. Use the Substitution Method

4. Example 2 Use the Substitution Method FURNITURE 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? Understand You are asked to find the number of each type of chair sold.

5. Example 2 Use the Substitution Method FURNITURE 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? 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. Plan

6. Example 2 Use the Substitution Method FURNITURE 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? x + y =48The total number of chairs sold was 48. 265x + 320y =13,930The total amount earned was $13,930.

7. Example 2 Use the Substitution Method 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. x + y =48First equation x=48 – ySubtract y from each side.

8. Example 2 Use the Substitution Method Solve Substitute 48 – y for x in the second equation. 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.

9. Example 2 Use the Substitution Method Now find the value of x. Substitute the value for y into either equation. 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.

11. Example 3 Solve by Using Elimination Use the elimination method to solve the system of equations. x + 2y = 10 x + y = 6

12. Example 3 Solve by Using Elimination Now find x by substituting 4 for y in either original equation. x + y=6Second equation x + 4=6Replace y with 4. x= 2Subtract 4 from each side. Answer:The solution is (2, 4).

13. Example 4 Solve the system of equations. x + 3y = 7 2x + 5y = 10 A. B.(1, 2) C.(–5, 4) D.no solution

14. Assignment – Pg. 141-144 #13, 14, 16, 29, 50, 53, 54, 58, 67, 76

15. Example 6 A.210 adult; 120 children B.120 adult; 210 children C.300 children; 30 adult D.300 children; 30 adult AMUSEMENT PARKS At Amy’s 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?