y = x + 4
y = 2x + 5
r + s = -6
r - s = -10
x = 4y
2x + 3y = 22
The sum of two numbers is 104. Their difference is 68.
Set up system and then solve.
What are the numbers?
x + y = 104
x - y = 68
What are 86 and 18?
Is the point a solution to the system?
No! The point lies on the DASHED line, so you cannot include it in the solution!
y = 3x - 2
y = -x - 2
The solution to the system:
8a + 5b = 9
2a - 5b = -4
What is (0.5, 1)?
y = x - 2
3x - y = 16
A shopper bought 6 shirts and 8 hats for $700. A week later, at the same prices, he bought 9 shirts and 6 hats for $660.
Set up system and solve.
What was the cost of one shirt?
6s+8h=700
9s+6h=660
What is $30?
Is the point a solution to the system?
Yes! This point lies in the shaded region.
(Hint: The tick marks on the graph go up by 5's!)
The answer to an equation or system of equations.
Solve the system by graphing:
y = -3x+2
x = -1
What is (-1, 5)
2x + 3y = 6
3x + 5y = 15
y = 3x - 1
7x + 2y = 37
Tickets to a football game cost $5.oo if purchased before the day of the game. They cost $7.50 if purchased at the game. For a particular game, 600 tickets were sold and the receipts were $3500.
Set up the system.
5x+7.50y=3500
x+y=600
Solve the system:
y>=-2/3x+2
y<2x-3
The solution to the system of equations by graphing
y = (1/3)x - 3
2x - y = 8
What is (3, -2)
2a - 4b = 12
-8a + 16b = -48
3s - 2t = 4
t = 2s - 1
The dimensions of a rectangle whose perimeter is 78 inches, when the length of the rectangle is twice its width.
Set up system and solve.
2l+2w=78
l=2w
What is 26x13?
Solve the system:
y+2x<3
y>=4
The solution to the system of equations:
y - 3x =10
y = 3x - 2
What is no solution?
(1/3)x + (1/4)y = 10
(1/3)x - (1/2)y = 4
t + u = 12
t = (1/3)u
If Jane has 36 coins totaling $3.00, and the coins are all nickels and quarters. Set up a system to decide how many of each coin she has?
n + q = 36
0.25q + 0.05n = 3.00
Oliver recieves a $80 gift card to spend at a store, he is buying records for his record player. New records cost $25 and used records cost $8. He wants to buy more than 5 records.
Set up the system
25n+8u<=80
n+u>5