Solve the System
Using Elimination
Using Elimination
Solve the System
Using Substitution
Using Substitution
Graphing Systems
Application of Linear Systems
100
x + 2y = 13
-x + y = 5
(1,6)
100
y = x + 1
x - y = 1
No Solution
100
When graphing a system, the solution lies at the point of _____.
Intersection
100
A group of 2 adults and 4 children pay $95 for admission to a water park. A different group of 3 adults and 7 children pay $155 for admission to the same water park. Write and solve a system of equations that can be used to determine the admission price to the water park for a adult and child.
Adult: $20
Child: $12.50
200
6x - 5y = 27
3x + 10y = -24
What is (2, -3)
200
Solve the system by using substitution
{(y=2x),(7x-y=15):}
(3, 6)
200
What does a system of linear equations with no solutions look like?
Two Parallel Lines
200
Sally plans to start a business selling t-shirts. She figures in one month it will cost her $210 in operating expenses plus $5 for every shirt. She plans to sell each shirt for $12. In one month how many t-shirts does Sally have to sell to break even?
30 t-shirts
300
2x + 5y = 11
4x + 3y = 1
what is (-2, 3)
300
3x - 30 = y
7y - 6 = 3x
(12, 6)
300
Solve the system by graphing:
{(y=2x+1),(y=3x-1):}
300
Isabella has 26 coins made up of quarters and nickels that have a value of $4.10. How many of each coin does Isabella have?
14 quarters and 12 nickels
400
Solve the system by using elimination:
{(4x+2y=14),(7x-3y=-8):}
(1, 5)
400
y - x = 2
y = -1/4 x + 7
(4, 6)
400
Graph the system of linear inequalities:
{(y=2x+3),(y=-1/2x-2):}
400
A farmhouse shelters 23 animals. Some are pigs and some are ducks. Altogether there are eighty legs. how many of each animal are there?
What is 6 ducks and 17 pigs.
500
Solve the system by using elimination:
8x + 3y = 4
5y = 7x - 34
What is (2, -4)
500
2x + y = 3
4x + 4y = 8
What is (1, 1)
500
Find a linear system that has the following:
a. The solution is (-3, 7)
b. Write equations in standard form.
c. One slope is positive. One slope is negative.
Answers will vary
500
Your task is to find the weight of all three reindeer (Rudolph, Donner, and Prancer) using a linear system of equations. When Rudolph and Donner were weighed together they weighed in at 345 kg. When Rudolph and Prancer were weighed together they weighed in at 332 kg. Prancer and Donner weighed in at 357 kg together.
Rudolph weighed 160 kg
Prancer weighed 172 kg
Donner weighed 185 kg