Graphing
Solve the system by graphing:
y = 3x + 5
y = x - 3
(1, -2)
Solve the system by elimination
3x - 2y = 1
2x + 2y = 14
(3, 4)
Solve the system by substitution
y = 4x
y = 2x + 6
(3, 12)
Solve the system of equations any way
y = 2x -3
y - 2x = -3
Infinitely many solutions
The Science Club needs to rent a bus for a field trip. Main Street Buses charges a $40 rental fee, plus $2 per mile. County Bus Line charges a $20 rental fee, plus $3 per mile. For what number of miles will the total charge be the same?
20 miles
Solve the system of equations by graphing :
y = x + 7
y = -2x - 2
(-3, 4)
Solve the system by elimination
x + y = 4
3x + y = 16
(6, -2)
Solve the system by substitution
y = x - 2
2x + y = 4
(2, 0)
Solve the system of equations any way
2x + y = 1
2x + y = -3
No solution
Maryann and Carlos are each saving for new scooters. So far, Maryann has $9 saved, and can earn $6 per hour babysitting. Carlos has $3 saved, and can earn $9 per hour working at his family's restaurant. After how many hours of work will Maryann and Carlos have saved the same amount?
2 hours
Solve the system of equations by graphing:
y = x + 4
y = -2x + 1
(-1, 3)
Solve the system by elimination
3x + 2y = -26
2x - 6y = -10
(-8, -1)
Solve the system by substitution
2x + y = -1
-x + y = -7
Solve the system of equations any way
y = 5x +2
y - 5x + 2
Infinitely many solutions
Brianna's family spent $134 on 2 adult tickets and 3 youth tickets at an amusement park. Max's family spent $146 on 3 adult tickets and 2 youth tickets. What is the price of a youth ticket?
$22
Solve the system of equations by graphing
y = x + 6
y = -3x + 6
(0, 6)
Solve the system by elimination
x + 3y = -14
2x - 4y = 32
(4, -6)
Solve the system by substitution
3x - 2y = 7
x + 3y = -5
(1, -2)
Solve the system of equations any way
y = -4x + 1
4x = -y - 6
infinitely many solutions
Carl bought 19 apples of 2 different varieties to make a pie. The total cost of the apples was $5.10. Granny Smith apples cost $0.25 each and Gala apples cost $0.30 each. How many of each type of apple did Carl buy?
7 Gala Apples, 12 Granny Smith Apples
Solve the system of equations by graphing
y = -5/3x + 3
y = 1/3x - 3
(3, -2)
4x - y = -5
-2x + 3y = 10
(-1/2, 3)
Solve the system by substitution
1/2x + 1/3y = 5
1/4x + y = 10
(4, 9)
Solve the system of equations in any way
x + y = 4
y - 4 = 1 - x
No solution
A professional organizer charges a $45 consultation fee, plus $20 per hour. Her competitor charges a $30 consultation fee, plus $26 per hour. Solve the system by substitution. For what number of hours will the total charge be the same.
2.5 hours