Systems of Equations and Inequalities Review

The sum of 2 numbers is 33.  The smaller number is 8 less than 7 times lager number.
Let x= the smaller number and y=the larger number. 
Pick which system of equations follows this problem.

• x=8-7y
  x+y=33

• x=7y-8
  x+y=33

• 7x+8y=33
  x+y=n

• 2+x=33
  x=8y-7

Pick the following inequality that relates to this graph:

• y<-2x+2

• y≤-2x+2

• y>-2x+2

• y≥-2x+2

You have a total of 17 coins.  All of your coins are nickels and dimes.  The total value of the coins is $1.35.  Which system of equations represents this situation?

• n+d=17
  .05n+.10d=1.35

• .05n+.10d=17
  n+d=1.35

• .25n+.10d=1.35
  n+d=17

Is (3,2) a solution to
3x-4y=1
x-y=0

• yes

• no

Solve the following system:
A farmer is in his field and knows he has 13 animals.  His animals are made up of chickens and cows.  The farmer can see that he has 34 legs in all but needs to know how many of each animal he has. 

• 4 cows, 9 chickens 

• 4 cows, 2 chickens

• 9 cows, 4 chickens

• 9 cows, 2 chickens 

An inequality using a ≤ or ≥ is graphed using a 

• solid line

• dashed line

• invisible line

• no line!

What is the solution to the system?

• (-1, 4)

• (3, 0)

• (4, 1)

• (0, -1)

Alexandra finds that she can give 3 haircuts and 2 hair dyes in 315 minutes. Giving 2 haircuts and 4 hair dyes takes 450 minutes.  Which system of equations represents the situation?

• 3x + 2y = 315
  2x + 4y = 450

• 3x + 2y = 450
  2x + 4y = 315

• 2x + 2y = 315
  3x + 4y = 450

Which point is a solution to the system of inequalities?

• (-8,2)

• (-3, 1)

• (0,6)

• (4, 3)

• A

• B

• C

• D