Word Problems
Jeremy buys two shirts and a jacket for $35. Jack also buys. He later buys two jackets and a shirt for $40. How much does a jacket or a shirt cost?
Jacket=$15
Shirt=$10
-x+2y=4
x+y=5
X=2
Y=3
Y=X-5
2x+5y=45
Y=5
X=10
Solve
Y= 2x+3
Y=-2x -1
(-1,1)
A system of Equations is either independent if it has one solution, or _____ if it has infinitely many solutions.
What is Dependent?
Big Bob has a bag full of dimes and quarters. The bag has a total of twelve coins, and the coins amount to $1.50. How many coins of each type does Big Bob have?
dimes=10
quarters=2
-2x+3y=15
4x-3y=-9
x=3
y=7
y=3x-18
y=x+3-7
x=7
y=3
Solve:
y=3x-5
y=1
(2,1)
What is substitution
A Game-stop has a start up cost of $5000. Each video-game has a cost of $2 to acquire, and a sale price of $10. How many video-games need to be sold to break even?
625 video-games need to be sold
y+2x=20.6
3y+x=21.8
x=8
y=4.6
y=1/2x+15
2x+3y=94
x=14
y=22
/lSolve:
y=-1/2x+1
y=-2x-2
(-2,2)
While linear equalities include an = sign, Linear ______ include a < or a > sign
What is linear inequality
A plane is flying from Atlanta to a small town, with a separate plane flying the same route but going from the town to Atlanta. The trip to the small town is flying with the tailwind and moves at 560 miles per hour. The trip flying against the tailwind moves at 490 miles per hour. How fast is the wind and the speed of the plane in miles/hour?
plane=525 miles/hour
wind=25 miles/hour
2x-3y=-38
-x+3y=61
x=23
y=28
y=2x-7
x+3y=31.5
x=7.5
y=8
Solve:
x=2
y=x+5
(2,7)
When solving a linear inequality, you are looking for an ordered pair, called a ______, that makes the inequality true
What is a Solution of an inequality
A theatre takes $80,000 to start up, and it takes $5,000 to put on a show. A sold out show makes $8,000. If every show sells out, how many full shows are required to break even?
27 shows
4x+3y=2
-2x+y=14
x=-4
y=6
5x+3y=204
2y=4x+142
x=9
y=53
Solve:
y=1/2x +7
y=-1+3/2x
(4,5)