Lines and Systems Review
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1 Lines and Systems Review SET 1 Question 1 Identify all points that are solutions to the system of equations represented by the graph: Question 2 Create a system of equations for each situation. Problem A: Hillary had 600 coins made up of quarters and dimes, totaling $ How many quarters and dimes does she have? Problem B: The perimeter of a rectangle is 34 inches. If the length is 2 inches more than twice the width, find the length and width of the rectangle. Problem C: The sum of two consecutive integers equals 199. Find the integers. Question 3 Create at least three systems of equations with the same solution as the system of equations below. 6x y = 12 9x + 8y = 11
2 Question 4 In your own words, state the definition of a solution to a system of equations. Question 5 Create a graph and a table of the equation x = 7. Find the rate of change and explain why your answer makes sense. Question 6 The graphs of f = 7x 8 and g = x + 3 meet at a single point. Find this point. Question 7 Find the y-intercept and rate of change of the equation represented by the ordered pairs below: (2, 3.6), (3, 3.4), (4, 3.2), (5, 3), (6, 2.8) Question 8 Is the point (4, 2) a solution to the inequality represented by the graph to the right? Explain. Find the linear inequality represented by the graph. Question 9 Solve the system of equations by substitution: y = 5x 4 2x + 4y = 17
3 Question 10 Based on the graph, find the interval with the greatest positive rate of change: Question 11 Mike made a table of a linear equation. Find the rate of change and fill out the rest of the table. x y Question 12 Create an equation and draw a graph of the equation y = 1 3 x + 7 Question 13 Matt and Ming are selling fruit for a school fundraiser. Customers can buy small boxes of oranges and large boxes of oranges. Matt sold 3 small boxes of oranges and 14 large boxes of oranges for a total of $203. Ming sold 11 small boxes of oranges and 11 large boxes of oranges for a total of $220. Find the cost each of one small box of oranges and one large box of oranges.
4 Question 14 If f = 7x 12 and g = x + 2, find the solution to f = g. Question 15 The figure on the right show the graphs of f and g. How many solutions satisfy the equation f = g? Explain your answer, using evidence from the graphs. Question 16 In the equation c = 5.25r + 125, if c represents the cost of manufacturing r radios, then explain what 5.25 is in terms of radio making. Explain what 125 is in terms of radio making. SET 2 Question 1 Create a system of equations for each situation. Problem A: A jar of coins contains six times as many quarters as dimes. If the total amount of money is $28.80, how many quarters and dimes are in the jar? Problem B: A rectangle is 3 times larger than its width. The perimeter is 44 cm. Find the dimensions of the rectangle. Problem C: The sum of consecutive even integers equals 202. Find the integers. Question 2 In your own words, state the definition of a system of equations or inequalities. Question 3 Find the y-intercept and rate of change of the equation represented by the ordered pairs below: (2, 5.5), (3, 5.25), (4, 5), (5, 4.75), (6, 4.5) Question 4 Solve the system of equations using the substitution method:
5 y + 4 = 2x 3x 2y = 1 Question 5 Create at least three systems of equations with the same solution as the system of equations below. x 10y = 0 7x + y = 12 Question 6 Create a graph and a table of the equation y = 7. Find the rate of change and explain why your answer makes sense. Question 7 Is the point (1, 2) a solution to the inequality represented by the graph to the right? Explain why or why not. Find the linear inequality represented by the graph. Question 8 The graphs of f = 2x + 3 and g = 1 x 6 meet at a single point. Find this point. 2 Question 9 Based on the graph, find the interval with the greatest rate of change: Question 10 Earl made a table of a linear equation. Find the rate of change and fill out the rest of the table. x y Question 12
6 Create an equation and draw a graph of the inequality y < 1 3 x + 7 Question 13 The senior classes at High School A and High School B planned separate trips to New York City. The senior class at High School A rented and filled 1 van and 6 buses with 372 students. High School B rented and filled 4 vans and 12 buses with 780 students. Each van and each bus carried the same number of students. How many students can a van carry? How about a bus? Question 14 If f = 1 x + 5 and g = x + 10, find the solution to f = g. 4 Question 15 The figure on the right show the graphs of f and g. How many solutions satisfy the equation f = g? Explain your answer, using evidence from the graphs. Question 16 The cost of airing a commercial on television is modeled by the function C = 110n + 900, where n is the number of times the commercial is aired. Describe what 110 and 900 might represent in real-world terms.
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