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 |