Solving Systems
Solve the following:
x+5y=10
-2x-6y=-8
What is (-5,3)?
Solve the following:
-4x-2y=-12
4x+8y=-24
What is (6,-6)?
Kristin spent $131 on shirts. Fancy shirts costs $28 and plain shirts cost $15. If she bought a total of 7 then how many of each kind did she buy?
x = # of fancy shirts
y = # of plain shirts
28x + 15y = 131 AND x + y = 7
She bought 2 fancy shirts and 5 plain shirts
Identify the unknowns in the problem below:
Trish is selling valentines and chocolates for Valentine's Day in order to make money for her class trip. She needs to make $500 and she is selling the valentines for $2 and the chocolates for $4.50. She is only selling the chocolates if you buy a valentine first. How many valentines and chocolates could she sell?
How many valentines she sells, how many chocolates she sells
A customer bought one cup of tea and two cups of coffee at a total cost of $2.80. Another customer bought two cups of tea and five cups of coffee at a total cost of $6.70. Find the cost of a cup of tea and a cup of coffee.
A cup of tea: $0.60
A cup of coffee: $1.10?
Solve the following:
-2x-3y=-13
x - y=4
What is (5,1)?
Solve the following:
3x + y = 9
4x - y = 5
There are 13 animals in the barn. Some are chickens and some are pigs. There are 40 legs in all. How many of each animal are there?
x = # of chickens y = # of pigs
x + y = 13 AND 2x + 4y = 40
There are 6 chickens and 7 pigs
Write a system of inequalities for the following problem:
Whenever the Lakers and the Rockets play a game of basketball, they score at least 120 points between the two teams. The Lakers always win, and they beat the Rockets by at least 5 points. What could be a potential score of a Lakers-Rockets game?
x= Lakers
y= Rockets
x + y >= 120
y + 5 >= x
A marine fish exhibition is held at the Singapore Expo. The entrance fees for 5 adults and 6 children are $67. How much would it cost a family of 12?
What is $50?
Solve the following:
-4x+3y=1
-4x+y=-13
What is (5,7)?
Solve the following:
4x+8y=20
-4x+2y=-30
What is (7, -1)?
A farmhouse shelters 10 animals. Some are pigs and some are ducks. Altogether there are 36 legs. How many of each animal are there?
x = # of pigs y = # of ducks
x + y = 10 AND 4x + 2y = 36
There are 8 Pigs and 2 Ducks
Write a system of inequalities for the problem below:
Marsha is buying plants and soil for her garden. The soil costs $4 per bag and the plants cost $10 each. She wants to buy at least 5 plants and she needs at least 1 bag of soil for every 5 plants she buys. She can spend no more than $100. How many plants and bags of soil can she buy?
b =bags of soil
p = plants
4B + 10P <= 100
5B > S
The sum of two integers is three times their difference. Thrice the smaller integer exceeds the larger integer by 4.
x = larger integer
y = smaller integer
What is (8,4)?
Solve the following:
x+y=3
-2x-y=-3
What is (0,3)?
Solve the following:.
8x+y=-27
-9x+4y=15
What is (-3, -3)?
A class of 195 students went on a field trip. They took 7 vehicles, some cars and some buses. Find the number of cars and the number of buses the took if each car holds 5 students and each bus holds 45 students.
x = # of cars y = # of buses
x + y = 7 AND 5x + 45y = 195
There are 4 Buses and 3 cars
Write a system of inequalities for the problem below:
You are tasked with proposing what new mixture of new cars the local police department should buy. They could get a Hybrid truck (holds 5 people, costs $20 per 100 miles) or a regular Van (holds 7 people, costs $15 per 100 miles). You want to be able to hold up to 100 people at a time and pay a maximum of $300 for those people per 100 miles. What are you going to do?
t = truck
v = van
5T + 7V >= 100
$20T + $15V <= $300
Without a calculator, solve the following:
y= 6x - 13
6x + 4y = 8
What is (2, -1)?
Solve the following:
x-y=3
7x-6y =20
What is (2,-1)?
Solve the following:
-10x+y=12
-2x-2y=-2
What is (-1, 2)?
A farmhouse shelters 11 animals. Some are goats and some are ducks. Altogether there are 34 legs. How many of each animal are there?
x = # of goats y = # of ducks
x + y = 11 AND 4x + 2y = 34
There are 5 ducks and 6 goats
Write a system of inequalities for the following problem:
You are tasked with proposing how best to run the local high schools, choosing between Charter and Public schools. Charter schools cost $8000 per student and usually hold 450 students. Public schools cost $9500 per student and can hold 1350 students. You need space for up to 22,000 students and can only spend $190,000,000. How many of each are you going to have?
c = charter school
p = public school
$8000C + $9500P <= $190,000,000
450C + 1350P >= 22000
Without your calculator, solve the following system:
-3x + 5y = 2
x + y = -6
What is (-4, -2)?