Substitution
Solve using substitution.
x + 2y =8
x = -5
x = -5, y = 6.5
Solve using elimination.
2x + 3y = 7
-2x + 4y = 14
x = -1
y = 3
y = 2x - 7
y = -7x +2
One solution
Lisa's school is selling tickets to the talent show. On the first day of sales the school sold 4 adult tickets and 5 student tickets for a total of $102. On the second day, the school made $126 selling 7 adult tickets and 5 student tickets. What was the cost of one adult ticket and one student ticket?
Adult - $8
Student - $14
y = -7x + 13
y = -1
x = 2
y = -1
2x + 3y = 5
2x + 4y = 9
x - -3.5
y = 4
y = 2x -3
y = 2x - 13
No solutions
Juan and Lea are selling pies for a fundraiser. Customers can buy apple & lemon pies. Juan sold 6 apple pies and 4 lemon pies for a total of $80. Lea sold 6 apple pies for 5 lemon pies for a total of $94. What is the cost of one apple pie and one lemon pie?
Apple - $4
Lemon - $14
3x = 8
3x + y = 15
x= 8/3
y = 7
2x + 3y = 7
3x - 3y = 3
x = 2
y = 1
3x + y = -10
3y =-x -10
One solution
The senior classes at Linden-McKinley and East High School planned separate trips to the water park. The senior class at Linden-McKinley rented and filled 14 vans and 16 buses with 1086 students. East High School rented and filled 10 vans and 13 buses with 870 students. Every van had the same number of students in it as did the buses. Find the number of students in each van and in each bus.
Van - 9 people
Bus - 60 people
y = 2x - 7
4 + y = 12
x = 7.5
y = 8
2x + 3y = 16
6x - 5y = 20
x = 5
y = 2
4y = x + 4
y = 1/4x + 1
Infinitely many solutions
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. After how many miles will the cost be the same for both taxi cabs?
y=.50x+4
y=0.25x+5
After 4 miles the cost will be the same.
2x + 4y = 20
x = 4
x = 4
y = -3
5x + 2y = 29
5x - 2y = 41
x = 7
y = -3
x - 4y = -12
5x - 20y = 60
No solutions
The drama club is running a lemonade stand to raise money for its new production. A local grocery store donated cans of lemonade and bottles of water. Cans of lemonade sell for $2 each and bottles of water sell for $1.50 each. The club needs to raise $570 to cover the cost of renting costumes. The students will accept a total of 360 cans and bottles. Write a system of that can be used to represent this situation then solve it.
System:
2x + 1.5y = 5702x + 1.5y = 570
x + y = 360x + y = 360
Solution: 60 cans of lemonade, 300 bottles of water