Systems of Equations in Context

Master systems of equations with practical word problems!

1. Solve the system of equations using elimination, substitution, or the Desmos graphing calculator. x + y = 5 3x + 2y = 14 (2,3) (0,5) (-1,6) (4,1) 2. Leola is thinking of two numbers. The difference between the numbers is 15. One number is six more than twice the other. Thomas decided to try to figure it out algebraically.He writes the following equations:x - y = 15y = 2x + 6Thomas solves the system using substitution. His work is shown below. x - y = 15x - (2x + 6) = 15x - 2x + 6 = 15-x = 9 x = -9Is his answer for the first variable correct? If not, what mistake did he make? He is correct. He is not correct. He did not substitute y into the first equation correctly. He is not correct. He did not distribute the negative to both terms inside the parenthesis. He is not correct. He switched his final answer to -9. 3. Which system represents the situation described above? a + m = 54a + m = 4 a + m = 54m = a + 4 a + m = 54a = m + 4 4. Which system represents the situation described above? c + b = 195c + b = 7 c + b = 7195b + 7c = 45 c + b = 75c + 45b = 195 5. Jaquille bought 2 large popcorn buckets and 4 small drinks for $20. Florence bought 2 large popcorn buckets and 2 small drinks for $14. What was the cost of the large popcorn and the small drink?Part 1: Type the equationsPart 2: Answer the question by solving the system. 6. Mr. Roberts purchased 20 concert tickets for a total of $225. The concert tickets cost $15 for adults and $10 for children under the age of 12. How many of each type of ticket did he purchase?Write and solve a system of equations to represent the given scenario. Use the variables “a” for adults and “c” for children.Part 1: Write the equationsPart 2: Solve the equations.