Transcript Algebra 2
Solve by Using Substitution Use substitution to solve the system of equations. x + 4y = 26 x – 5y = –10 Solve the first equation for x in terms of y. x + 4y = 26 x = 26 – 4y First equation Subtract 4y from each side. Solve by Using Substitution Substitute 26 – 4y for x in the second equation and solve for y. x – 5y = –10 26 – 4y – 5y = –10 –9y = –36 y=4 Second equation Substitute 26 – 4y for x. Subtract 26 from each side. Divide each side by –9. Solve by Using Substitution Now substitute the value for y in either of the original equations and solve for x. x + 4y = 26 x + 4(4) = 26 x + 16 = 26 x = 10 First equation Replace y with 4. Simplify. Subtract 16 from each side. Answer: The solution of the system is (10, 4). Solve the system of equations using substitution. What is the solution to the system of equations? x – 3y = 2 x + 7y = 12 D. (5, 1) C. C D. D 0% 0% 0% 0% D B C C. (8, 2) B. B B. A. A A A. (1, 5) Solve by Substitution 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 You are asked to find the number of each type of chair sold. Solve by Substitution Solve the Test Item 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. x + y = 48 265x + 320y = 13,930 The total number of chairs sold was 48. The total amount earned was $13,930. Solve by Substitution 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. x + y = 48 x = 48 – y First equation Subtract y from each side. Solve by Substitution Step 3 Substitute 48 – y for x in the second equation. 265x + 320y = 13,930 265(48 – y) + 320y = 13,930 12,720 – 265y + 320y = 13,930 55y = 1210 y = 22 Second equation Substitute 48 – y for x. Distributive Property Simplify. Divide each side by 55. Solve by Substitution Step 4 Now find the value of x. Substitute the value for y into either equation. x + y = 48 x + 22 = 48 x = 26 First equation Replace y with 22. Subtract 22 from each side. Answer: They sold 26 rocking chairs and 22 Adirondack chairs. D C B A 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? A. A A. 210 adult; 120 children B. B B. 120 adult; 210 children C. C C. 300 children; 30 adult 0% 0% 0% 0% D. D D. 300 children; 30 adult