Linear Functions Review

Linear Equations

100

Find the solution to the system, 

y = -x

y = 2/5x - 7 

(5, -5)

200

Find the solution, 

y = -2/3x + 2

y = 1/2x - 5

(6, -2)

300

Using substitution, what would be the easiest first step to solve for, 

3x + 2y = 10

-3x + y = 14

BOUNS solve this using Substitution

Solve for y in the second equations. 

BOUNS (-2, 8)

400

Using elimination what would be the first step to solve, 

-x +3y = 5

-x -3y = 7

And which variable are you eliminating? 

Add the equations to get rid of the y values. 

500

Using elimination, what would be the easiest first step to solve, 

5x + 3y = 8

2x + y = 3

*BOUNS solve using elimination* 

Multiplying the bottom equations by -3 to eliminate the y values. 

Bonus (1,1)

Linear Inequalities

100

Is (2, 6) a solution to this system of inequalities?

y ≥ 6x + 10
y < x + 9

NO

200

Is (5, -5) a solution to this system of inequalities?

2x + 18y ≤ 20
7x + y > 8

Yes

300

What are the vertices of 

y ≤ -x +6

x ≥ 0

y ≥  0 

(0,6)

(0,0)

(6,0)

400

What is the vertices for, 

y ≥  -x +10

x ≤ 9

y ≤ 1/2 x +7

y≤ 10

(2,8)

(6,10)

(9,10)

(9,1)

500

Find the verticies, 

0≤ 2x +3y +15 

-20 ≤  2y + 3x

7x +5y ≤ -25

3x + 5y ≤ -5

(-10,5)

(-5,2)

(-6,-1)

(0,-5)

Word Problems

100

A rental car costs $30 per day plus $0.20 per mile driven. Write the equation to find the total cost, y, for x miles driven in a single day.

What is y = 0.2x+30

200

An attorney charges a fixed fee of $250 for an initial meeting and $150 per hour for all hours worked after that.  

a) What is the value of the y intercept and slope?

b) What would the slope intercept equations look like?

a) 250 and 150x

b) y=150x+250

300

Several times a week, Chuck goes to the gym to run and swim. When running, he burns 35 calories per minute, and when he swims he burns 30 calories per minute. He found a way to burn 730 calories after exercising for a total of 23 minutes. How long does he spend at each activity? use X and Y as variables. 

x+y=23

35x+30y=730

400

You are at school, 12 miles away from home. You start walking home with your friends at a speed of 3 miles per hour towards your home.

a. Write an equation that represents your distance from home (y) after (x) hours.

b. How many hours does it take to get home? 

a. y = -3x + 12

b. 4 hours

500

There are 18 performers in the Flea Circus. However, none of them are actually fleas, they are either spiders (with 8 legs) or bugs (with 6 legs). Mr. Barnum wants to provide every performer with tiny shoes for the ends of their many legs. If this requires a total of 130 shoes how many spiders and bugs are in the circus? Create a system and solve. 

x+y=18

8x+6y=130

Solution (11,7)

Linear Programming

100

Using the vertices (0,0) (1,1) and (2,5) what is the max and min for the equation 

T = 2x + 3y

Max = 19

Min = 0

200

what is the value of the x and y for the min value, 

P = 8x +4y

y ≥ 1/5 x +4

x ≥ 5

y ≤ -1/5 x +8

(5 , 5)

300

Label the Min value and the x and y values. 

y ≤ -2x +9

y ≤ 6x +1

y ≥ 2x +1

R = -10x +3y

Min -5 at (2,5)

400

What is the max and min values and their x and y values of 

y ≥ 0

x ≥ 0

y ≤ -x + 4

C = x - 12y

Max = 4 at (4,0)

Min = -48 at (0,4)

500

Find the vertices and then find the max value using C= -4x - 5y

0≤ 2x +3y +15 

-20 ≤  2y + 3x

7x +5y ≤ -25

3x + 5y ≤ -5

max = 29

Matrices

100

What is the augmented matrices of the following,

x + 3y = 7

-x -5y = 2

1 3 7

-1 -5 2

200

What is the augmented matrices of the following, 

x + 2y +z = 5

x + 3z = 7

3x -2y +z = 3

1 2 1 5 

1 3 0 7 

3 -2 1 3 

300

What is the augmented matrices and the RREF of the following, 

2x +2y -z = -3

x + y +z = 6

3x -2y -z = 8

2 2 -1 -3

1 1 1 6

3 -2 -1 8 

1 0 0 3

0 1 0 -2

0 0 1 5

400

What is the RREF and the solution to the system of, 

x - y + 2z = -1

-3x + 3y +5z = 3

2x - 2y = -2

1 -1 0 -1

0 0 1 0 

0 0 0 0 

Infinite solutions 

500

Write out the Augmented Matrix, the RREF, and the Solution to, 

3x = -12 -3y

-2y + 2z = 4x -14

x = -3y -2z + 11

 3 3 0 -12

-4 -2 2 -14

1 3 2 11

1 0 -1 0

0 1 1 0 

0 0 0 1

No solution