Solve by Graphing
y = 2x − 3
y = x + 2
(5,7)
y = − 3x − 7
y = x + 9
(-4,5)
x − 2y = − 7
3x + 2y = 3
(-1,3)
x + 2y = − 5
x − 2y = − 5
(-5,0)
A gift basket that contains jars of jam and packages of bread mix costs $45. There are 8 items in the basket. Jars of jam cost $6 each, and packages of bread mix cost $5 each. Write and solve a system of linear equations to find the number of jars of jam and the number of packages of bread mix in the gift basket.
x + y = 8
6x + 5y = 45
5 jars of jam, 3 packages of bread mix
y = −x + 4
x + 3y = 0
(6,-2)
1/2 x + y = − 4
y = 2x + 16
(-8,0)
2x + 7y = 1
2x − 4y = 12
(4,-1)
8x − 2y = 16
− 4x + y = 8
no solution
You download a digital album for $10. Then you and your friend download the same number of individual songs for $0.99 each. Write a system of linear equations that represents this situation. Will you and your friend spend the same amount of money?
y = 0.99x + 10
y = 0.99x
no; Because you paid $10 before buying the same number of songs at the same price, you spend $10 more.
x − y = − 2
2x − 3y = − 2
(-4,-2)
−x + 5y = 28
x + 3y = 20
(2,6)
5x + 8y = − 2
− 2x + 3y = 7
(-2,1)
3x − 2y = 1
9x − 6y = 3
many solutions. all points on the line
A drama club earns $1040 from a production. It sells a total of 64 adult tickets and 132 student tickets. An adult ticket costs twice as much as a student ticket.
x = 2y
64x + 132y = 1040
adult tickets: $8; student tickets: $4