Fractions!!!!
x + 1/3y = 5
x - 1/2y = 0
(3,6)
x = y + 1
2x + y = 23
(8,7)
x + 3y = -2
x - 3y = 16
(7,-3)
Without graphing or solving, determine the number of solutions to the system. Explain your reasoning.
y = 5x - 9
y = 5x + 9
no solution; the lines are parallel
Your family is buying tickets for an amusement park. Child tickets are $20 each, and adult tickets are $50. Your family buys a total of 10 tickets and spends $320. How many of each ticket you purchase?
4 adult tickets and 6 child tickets
x+1/2y = 11
x - 1/8 y = 1
(3,16)
y = 2x - 4
7x - 2y = 5
(-1,-6)
2x - y = 9
4x + y = 21
(5,1)
Without graphing or solving, determine the number of solutions to the system. Explain your reasoning.
y = 6x + 2
y = 3x + 1
1 solution; Different slopes
The width of a rectangle is 8 cm more than 3 times the length. The perimeter of the rectangle is 240 cm. Write a system of equations to model the situation. What is the length and the width of the rectangle?
L = 28 cm
W = 92 cm
x + 1/2y = 8
x + 1/4y = 6
(4,8)
-4x - 2y = 0
y = 1/2x -5
(2,-4)
-5x + 2y = 13
5x + y = -1
(-1,4)
determine the number of solutions to the system. Explain your reasoning.
y = 8x - 2
y = -8x -2
1 solution; different slopes
You are planning a party and buy a total of 50 hamburgers and hotdogs for $90. You pay $2 per hamburger and $1.50 per hotdog. How many of each did you buy?
30 hamburgers and 20 hotdogs
x + 1/10y = 5
x - 1/2y = -1
(4,10)
x = 5y + 3
2x + 4y = -1
(it will be a fraction or decimal)
(1/2, - 1/2) or (.5, -.5)
-6x + 5y = 25
-2x - 4y =14
(-5,-1)
determine the number of solutions to the system. Explain your reasoning.
4y - 4x= 8
y = x + 2
infinitely many solutions; same equations
The width of a rectangle is 2.8 cm more than 5 times the length. The perimeter of the rectangle is 53.6 cm. Write a system of equations to model the situation. What is the length and the width of the rectangle?
(One answer is a decimal)
L = 4 cm
W = 22.8 cm
x -1/3y = 1
x - 1/2y = -1
(5,12)
y = -4x + 2
y=6x - 8
(1, -2)
-4x - 2y = 14
-10x + 7y = -25
(-1,-5)
Without graphing or solving, determine the number of solutions to the system. Explain your reasoning.
2x - 4y = 10
-12x + 24y = -60
Infinitely many solutions; same equation
The width of a rectangle is 5 cm less than twice the length. The perimeter of the rectangle is 53.6 cm. Write a system of equations to model the situation. What is the length and the width of the rectangle?
L = 12 cm
W = 19 cm