Systems by Graphing Worksheets Grade 8

1. Isabella is organizing a school bake sale and needs to choose between two pricing strategies for her team. In Strategy A, they charge a $40 base fee for table rental plus $2.50 per baked item sold. In Strategy B, they charge a $10 base fee for table rental plus $3.75 per baked item sold. Isabella wants to graph both cost equations on the same coordinate plane to determine for how many baked items the total cost would be the same with both strategies. Let x represent the number of baked items sold and y represent the total cost in dollars. After graphing the system of equations, what is the point of intersection? Write your answer as an ordered pair (x, y).
2. A scientist is tracking the growth of two different bacteria cultures. Culture A starts with 800 cells and grows at a rate of 300 cells per hour. Culture B starts with 2,000 cells and grows at a rate of 100 cells per hour. After how many hours will both cultures have the same number of cells?
3. y = 3x - 4 and y = -2x + 6

…and 3 more problems

1. y = 5x - 8 and y = -2x + 6
2. Emma is planning a school trip to the science museum and needs to choose between two transportation companies. Speedy Buses charges a $200 flat fee plus $8 per student. Reliable Coaches charges a $50 flat fee plus $12 per student. Emma wants to graph both cost equations to determine for how many students the total cost would be the same with both companies. Let x represent the number of students and y represent the total cost in dollars. After graphing the system of equations, what is the point of intersection?
3. Liam is planning a school fundraiser selling t-shirts and hoodies. The t-shirts cost $8 each and the hoodies cost $15 each. He needs to raise exactly $500. If he sells 40 items in total, how many of each type did he sell?

…and 4 more problems

1. Maya is organizing a community garden and needs to plan the planting of tomatoes and peppers. She has space for exactly 30 plants total. Tomatoes require 2 square feet each and peppers require 1 square foot each, and the total garden space is 45 square feet. If x represents the number of tomato plants and y represents the number of pepper plants, how many of each should Maya plant to use all her space efficiently?
2. y = 2x - 3 and y = -x + 6
3. A rectangular garden is drawn on a coordinate plane with corners at (2, 1), (8, 1), (8, 5), and (2, 5). A diagonal path is drawn from (2, 1) to (8, 5), creating two triangular sections. What is the area of one of these triangular sections?

…and 3 more problems