System of Equations & Inequalities

Systems and Inequalities Review

Quick overview of last month

Solving Systems by Substitution

look for or create a y= or x=

Multiple Choice

Which correctly sets up the first step to solve the system by substitution?
 
5x + 4y= −14
y = −7x − 15  

• $$5x+4\left(-7x-15\right)=-14$$  

• $$5\left(-7x-15\right)+4y=-14$$  
  

• $$5x+4y=-7x-15$$  
  

• $$5x+7x-15=-14$$  
  

Solving Systems by Elimination

look for or create a zero pair with a variable

Multiple Choice

Which is the correct result after performing the first step of solving by elimination?

4x+9y=28

-4x-y=-28

• $$10y=56$$
  

• $$No\ Solution$$
  

• $$8x+8y=0$$
  

• $$8y=0$$

Solving Systems by Graphing

Multiple Choice

What is the solution to the system?

• (0, 3)

• (1, -1)

• (-3, 1)

• (1, 3)

Multiple Choice

How many solutions will this system have?

• No solution

• One Solution

• I Don't Know

• Infinitely Many Solutions

Multiple Choice

When you graph the exact same equation twice,

• you will have no solution.

• you will have one solution.

• you will have infinite solutions.

• you will graph a giraffe.

Multiple Choice

When you graph the exact same equation twice,

• you will have no solution.

• you will have one solution.

• you will have infinite solutions.

• you will graph a giraffe.

Multiple Choice

^{What is the solution?}

• 1

• -2

• (1, 2)

• (1, -1)

Multiple Choice

Is (0, 16) a solution to the system of equations?
-3x=4y+2
2y=4x+32

• Yes, it is a solution to the system of equations

• No, it only satisfies the first equation, and fails to satisfy the second.

• No, it only satisfies the second equation, and fails to satisfy the first.

• No, it fails to satisfy both equations

Multiple Choice

Is (-2,7) a solution to the system of equations?
y=4x+15
-3x+5y=41

• Yes, it is a solution to the system of equations

• No, it only satisfies the first equation, and fails to satisfy the second.

• No, it only satisfies the second equation, and fails to satisfy the first.

• No, it fails to satisfy both equations

Graphing Linear Inequalities

shading rules

Multiple Choice

Select the correct graph for each inequality.

• A
• B
• C
• D

Multiple Choice

Select the correct graph for each inequality.

• A
• B
• C
• _D

Multiple Choice

Which point is NOT a solution?

• (0,1)

• (0,2)

• (-2,0)

• (2,0)

Multiple Choice

Determine if (0, 1) is a solution to $$y>-6x+1$$  .

• (0,1) is a solution

• (0, 1) is not a solution.

Multiple Choice

What is the solution to the system?

• (0, 3)
• (1, -1)
• (-3, 1)
• (1, 3)

Multiple Choice

Is (-2,4) a solution to the system?

• Solution
• Not a solution

Multiple Choice

Which of the following is a solution to the systems of inequalities?

• (0, -2)

• (-3, 0)

• (-3, 2)

• (1, 1)

Multiple Choice

Identify the graph represented by the following system of inequalities.

2x - y > 4

4x + 2y < 6

Multiple Choice

Solve the system of inequalities by graphing.

Multiple Choice

A sporting goods store sells left haded (x) and right handed (y) gloves. In one month, 12 gloves were sold for a total of $561. Right handed gloves cost $45 each and left handed gloves cost $52. Which system could be solved to determine the number of each type of glove sold?

• x + y = 561
  45x+52y=12
• x + y = 12
  52x+45y=561
• x + y = 12
  45x+52y=561
• x + y = 561
  52x+45y=12

Multiple Choice

Cullin needs to save at least $100 for homecoming. He works 2 jobs earning $8/hour at Culvers and $25/hour mowing lawns. He only has time to work 14 hours before homecoming.

• x + y ≥ 25

  x + y ≤ 8

• 100x + 25 y ≤ 100

  2x + 8y ≤ 14

• x + y ≥ 100

  8x + 25y ≤ 14

• 8x + 25y ≥ 100

  x + y ≤ 14

Multiple Choice

Write the system of inequalities

Carlos works at a movie theater selling tickets. The theater has 300 seats and charges $7.50 for adults and $5.50 for children. The theater expects to make at least $2000 for each showing

• x+y≤300

  7.5x+5.5y≥2000

• x+y<300

  7.5x+5.5y≥2000

• x+y≤300

  7.5x+5.5y≤2000

• x+y>2000

  7.5x+5.5y≤300

Multiple Choice

In other words...what are the vertices of the feasible region?

• (0, 0), (0, 6), (6, 2), (8, 0)

• (0, 0), (6, 0), (2, 6), (0, 8)

Multiple Choice

A farmer can plant up to 6 acres of land with soybeans and corn. Her use of a necessary pesticide is limited by federal regulations to 15 gallons for her entire 6 acres. Soybeans require 2 gallons of pesticide for every acre planted and corn requires 3 gallons per acre. The profit the farmer makes by earning $4,000 for every acre of soybeans he plants and $3,000 for every acre he plants with barley can be modeled by P=4000x+3000y .  If x represents acres of soybeans and y represents acres of corns, which inequalities represent the possible solutions to her situation?

• x≥0
  y≥0
  x+y≥6 
  3x+2y≥15
• x≥0 
  y≥0 
  x+y≤6
  2x+3y≤15
• x≥0 
  y≥0 
  4000x+y≤6
  2x+600y≤15
• P=4000x+3000y

Multiple Choice

Solve:
y = -1x - 5
4x - 8y = 4

• (-3, -2)
• (5, -7)
• (3, 9)
• (-5, 4)

Multiple Choice

Solve:
x = -3y - 17
2x + 3y = -7

• (1, -20)
• (3, 0)
• (-5, -2)
• (10 , -9)

Multiple Choice

Solve:
y=8x+1
y=6x+3

• (1, 9)
• (4, 14)
• (0, 1)
• (2, 4)

Multiple Choice

Solve the system of Equation (x,y)
3x + y = –14
–2x – y = 9

• (-5,1)
• (5,-1)
• (1,4)
• (-1,4)

Multiple Choice

Solve the system of Equation (x,y)
–2x + y = 10
4x – y = –14  

• (1,5)
• (6,2)
• (-2,6)
• (4,6)

Multiple Choice

What is the solution?

• No solution
• (0, 2)
• (0, -4)
• (3, -3)

Multiple Choice

What is the solution to this system?
x - y = 6
y= 2x - 5

• (1,3)
• (-1,3)
• (-1,-7)
• (1,-7)

Multiple Choice

Solve the system of equations.

y = -5x

x + 3y = 28

• (-6, 30)

• (-2, 10)

• (44, 39)

• No solution

Multiple Choice

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

• (0,-1)
• (0,3)
• (4,0)
• (6,-2)

Multiple Choice

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