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Solving Systems of Equations Answer Key

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Solution or Not?
#1 Is this ordered pair a solution of x-y = -3 and 2x + y = 0 (-1, 2) Yes
#2 Is this ordered pair a solution of x=2y+1 and y=x (-1, -1) Yes
#3 Is this ordered pair a solution of 4x-y=-3 and 3y-6x=6 (2,11) No
#4 What does it mean if (3,2) is a solution of y=x-1 and y=-x+5 (3,2) is where the lines intersect
#5 Tell whether (-5, -6) is a solution of x-2y = 7 and y-x=2 No
Solving Systems by Graphing
#1 Solve y=x-3 and y=-x+5 by graphing (4,1)
#2 Solve 4x+y=-1 and y-4=x by graphing (-1, 3)
#3 Solve y-2=1/3x and 3y=-2x-3 by graphing (-3, 1)
#4 Solve y-3x =2 and y= -2x-8 by graphing (-2, -4)
#5 Solve y-5 = -1/2x and x=y-2 by graphing (2, 4)
Solving Systems by Substitution
#1 Solve y=x +1 and x + y = 7 by substitution (3, 4)
#2 Solve y=x+3 and 2x+y=9 by substitution (2, 5)
#3 Solve y-2=3x and 3x-2y= -13 by substitution (3, 11)
#4 Solve 3x - 2y = 4 and x + 4y = 34 by substitution (6, 7)
#5 Solve 3y -4x = 29 and 2y + 5x = 4 by substitution (-2, 7)
Special Cases
#1 What is the solution of -4x + y =1 and 2y - 2 = 8x Infinitely Many Solutions
#2 What is the solution of 8y - 6x = 48 and 2y = 3/2 x -12 No Solution
#3 What is the solution of y = 2/3x +7 and 3y = 2x - 3 No Solution
#4 What is the solution of 5y - 4x = -5 and 10y + 10 = 8x Infinitely Many Solutions
#5 How many solutions does y = -6x + 10 and y = -6x + 3 have 0 solutions
Word Problems
#1 Leslie joins a fitenss club that has a membership fee of $20 plus $15 per month. Rashad's club has a fee of $40 and charges $10 per month. In how many months will the two clubs cost the same? 4 months
#2 Tank A contains 35 gallons of water and is increasing at a rate of 5 gallons per minute. Tank B contains 100 gallons of water and is decreasing at a rate of 8 gallons per minute. In how many minutes will the tanks contain the same amount of water? How much water will that be? 5 min; 60 gal
#3 Taxi company A charges $4 plus $0.50 per mile. Taxi company B charges $5 plus $0.25 per mile. Write a system of equations that could be used to represent this situation. y = 0.5 x + 4 and y = 0.25x + 5
#4 The sum of two numbers is 50. The first number is 43 less that twice the second number. Write and solve a system of equations to find the two numbers. x + y = 50 and x = 2y - 43 19 and 31
#5 Sally spent $14.85 to by 13 flowers. She bought lilies, which cost $1.25 and tulips, which cost $0.90 each. How many of each flower did sally buy? 9 lilies, 4 tulips
Final Question
Matt has $100 in a checking account and deposits $20 per month. Ben has $80 in a checking account and deposits $30 per month. Will the accouonts ever have the same balance? Explain Yes, the graphs have two different slopes, so they will intersect