Systems of Equations

Word Problems

100

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

200

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

300

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

400

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

500

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

Elimination

100

rffft-x+2y=4

x+y=5

X=2

Y=3

200

-2x+3y=15

4x-3y=-9

x=3

y=7

300

y+2x=20.6

3y+x=21.8

x=8

y=4.6

400

2x-3y=-38

-x+3y=61

x=23

y=28

500

4x+3y=2

-2x+y=14

x=-4

y=6

Substitution

100

Y=X-5

2x+5y=45

Y=5

X=10

200

y=3x-18

y=x+3-7

x=7

y=3

300

y=1/2x+15

2x+3y=94

x=14

y=22

400

y=2x-7

x+3y=31.5

x=7.5

y=8

500

5x+3y=204

2y=4x+142

x=9

y=53

Graphing

100

Solve

Y= 2x+3

Y=-2x -1

(-1,1)

200

Solve:

y=3x-5

y=1

(2,1)

300

/lSolve:

y=-1/2x+1

y=-2x-2

(-2,2)

400

Solve:

x=2

y=x+5

(2,7)

500

Solve:

y=1/2x +7

y=-1+3/2x

(4,5)

Vocab

100

A system of Equations is either independent if it has one solution, or _____ if it has infinitely many solutions.

What is Dependent?

200

The three ways to solve systems of equations are graphing, ____, and elimination

What is substitution

300

While linear equalities include an = sign, Linear ______ include a < or a > sign

What is linear inequality

400

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

500

When you have multiple linear inequalities, it is called this.

A system of linear inequalities.