Systems of Equations and Inequalities

What is the solution to the system?

• (0, 3)

• (1, -1)

• (-3, 1)

• (1, 3)

Solve the system by substitution.  

5x + 4y= −14

y +15 =  −7x  

• (-2, -1)

• (1, -2)

• (-2, 1)

• (-1, -2)

Does the system have one, none or infinite solutions?
8x + 4y = 12
y = -2x + 3

• (0,3)

• (3,0)

• No solution(parallel lines)

• Infinitely many solutions

Caitlin won a bag full of money! She has 49 bills in all. She counts $1,430. There are $20 dollar bills and $50 dollar bills. How many of each bill does Caitlin have?
WRITE a system where T= # of $20 and F = # of $50.

• T + F = 1430
  20T + 50F = 49

• T+ F = 49
  10T + 5F = 1430 

• T + F = 49
  20T + 50F  = 1430

• T + F = 49
  T + F = 1430

On Monday Joe bought 10 cups of coffee and 5 doughnuts for his office at the cost of $16.50.  It turns out that the doughnuts were more popular than the coffee.  On Tuesday he bought 5 cups of coffee and 10 doughnuts for a total of $14.25.  Which equations could be used to determine the cost of the coffee? 

• 10c + 5d = 14.25
  5c + 10d = 16.50

• 10c + 5d = 16.50
  5c + 10d = 14.25

• c + d = 10
  5c + 10d = 16.50

• c + d = 5
  5c + 10d = 16.50

Your family goes to a restaurant for dinner. There are 6 people in your family. Some order the chicken dinner for $14.80, and some order steak for $17. If the total bill was $91, which system best represents the situation? 

• x + y = 6
  14.80x + 17y = 91

• x + y = 91
  14.80x + 17y = 6

• x + y = 6
  14.80y + 17x = 91

• x + y = 91
  14.80x+ 17y = 6

Which of the following is not a solution to this system of inequalities?

• (0,-1)

• (0,3)

• (4,0)

• (6,-2)

Which system of inequalities is shown?

• y ≥ -x - 1
  y < x + 4

• y < -x - 1
   y ≥ x + 4

• y > -x - 1
  y ≥ x + 4

• y > -x - 1
  y ≥ x + 3

Solve by substitution
x= -7y+6
-2x+2y=4

• (-1,1)

• (-6,-1)

• (-1,-6)

• (-1,6)

Solve by substitution
y= 4x-13
-5x+8y=-23

• (-1,-3)

• No Solution

• (-1,3)

• (3,-1)