Solving by Elimination
3x−y>6
y−2x>9
Find the Solution to the following System of Inequalities Using Elimination
x>15
Which of the following is a possible value of x given the system of inequalities below?
3x+4y > 54
-4x+2y < 10
Use Substitution Method
x = 5
Question: A store sells two types of pens, A and B. Pen A costs $2 each, and Pen B costs $3 each. A customer wants to spend no more than $10 on pens. Write a system of inequalities to represent this situation. Let x be the number of Pen A and y be the number of Pen B.
2x + 3y ≤10
x ≥ 0, y ≥ 0
A furniture manufacturer produces two types of chairs, Wooden and Metal. Each Wooden chair requires 5 hours of labor and 2 units of wood, while each Metal chair requires 3 hours of labor and 4 units of wood. The company has no more than 40 hours of labor and no more than 30 units of wood available. Write a system of inequalities to represent this situation and find the maximum profit the company can make if the profit per Wooden chair is $30 and per Metal chair is $40. Let x be the number of Wooden chairs and y be the number of Metal chairs.
5x + 3y ≤40
2x + 4y ≤30
x ≥ 0, y ≥ 0
Maximum profit: $290 (5 Wooden chairs, 5 Metal chairs)
x+y>9
x−y>3
Solve the following Systems of Inequalities by Using the Elimination Method
x>6
Which of the following set of coordinates is within the graphed solution set for the system of inequalities below?
x+2y > 16
-3x+y < 1
Use Substitution
(3, 8)
A company produces two types of chairs, Standard and Deluxe. Each Standard chair requires 3 hours of labor, and each Deluxe chair requires 5 hours of labor. The company has no more than 80 hours of labor available each week. Write a system of inequalities to represent this situation and find the maximum number of chairs the company can produce. Let x be the number of Standard chairs and y be the number of Deluxe chairs
3x + 5y ≤ 80
x ≥ 0, y ≥ 0
Maximum chairs: 16 (0 Standard chairs, 16 Deluxe chairs)
A catering company offers two types of meal plans, Standard and Deluxe. Each Standard meal plan requires 2 hours of preparation and 3 units of ingredients, while each Deluxe meal plan requires 4 hours of preparation and 5 units of ingredients. The company has no more than 40 hours of preparation time and no more than 60 units of ingredients available. Write a system of inequalities to represent this situation and find the maximum revenue the company can generate if the revenue per Standard plan is $50 and per Deluxe plan is $80. Let x be the number of Standard meal plans and y be the number of Deluxe meal plans.
2x + 4y ≤ 40
3x + 5y ≤ 60
x ≥ 0, y ≥ 0
Maximum revenue: $550 (10 Standard plans, 6 Deluxe plans)
x>3y−2
x>10−y
Solve the following Systems of Inequalities by Using the Elimination Method
x>7
Solve Using Substitutution. Find x and y
x + y < 15
3x + 7y < 18
(5,10)
A car rental company offers two types of cars, Economy and Luxury. Renting an Economy car costs $30 per day, and renting a Luxury car costs $50 per day. A customer wants to spend no more than $200 on car rental. Write a system of inequalities to represent this situation. Let x be the number of Economy cars and y be the number of Luxury cars.
30x + 50y ≤ 200
x ≥ 0, y ≥ 0
A farmer has a total of 60 acres of land available for planting two crops, Corn and Soybeans. Each acre of Corn requires 2 units of fertilizer and 1 unit of pesticide, while each acre of Soybeans requires 1 unit of fertilizer and 2 units of pesticide. The farmer has no more than 100 units of fertilizer and no more than 90 units of pesticide available. Write a system of inequalities to represent this situation and find the maximum profit the farmer can make if the profit per acre of Corn is $300 and per acre of Soybeans is $200. Let x be the number of acres of Corn and y be the number of acres of Soybeans.
2x + y ≤ 100
x + 2y ≤ 90
x ≥ 0, y ≥ 0
Maximum profit: $4500 (30 acres of Corn, 30 acres of Soybeans)
y>3x+2
3x>8
Solve the following Systems of Inequalities by Using the Elimination Method
y>10
Solve the System of Inequalities by Substitution
y ≤ 2x + 3
y ≥ -x + 1
Answer: x ≥ −1, y ≥ −1
A farmer has a total of 50 acres of land available for planting two crops, Wheat and Barley. Each acre of Wheat requires 2 units of fertilizer, and each acre of Barley requires 3 units of fertilizer. The farmer has no more than 120 units of fertilizer available. Write a system of inequalities to represent this situation and find the maximum yield of each crop. Let x be the number of acres of Wheat and y be the number of acres of Barley.
2x + 3y ≤120
x ≥ 0, y ≥ 0
Maximum yield: Wheat - 40 acres, Barley - 0 acres
2x−3y>8
y>2x−5
Solve the following Systems of Inequalities by Using the Elimination Method
y<−3/2
y ≤ x + 2
y ≥ −2x + 1
Answer: x ≤ 34, y ≥ 12
A company produces two types of shirts, Plain and Printed. Each Plain shirt requires 2 units of fabric, and each Printed shirt requires 3 units of fabric. The company has no more than 300 units of fabric available. Write a system of inequalities to represent this situation and find the maximum number of shirts the company can produce. Let x be the number of Plain shirts and y be the number of Printed shirts.
2x + 3y ≤300
x ≥ 0, y ≥ 0
Maximum shirts: 100 (0 Plain shirts, 100 Printed shirts)