Applications of Linear Inequalities

What is the purpose of using systems of equations in real-world problems?

• To find the slope of a line

• To graph equations in a digital environment

• To solve problems with multiple variables and constraints

• To find the y-intercept

Which of the following is a real-world example of a system of equations?

• Finding the area of a rectangle

• Determining the cost of two items with different prices

• Solving for one unknown variable

• Calculating the exact speed of a car

Anna buys pens for $2 and pencils for $5. She buys 7 items and spends $26. Which system of equations represents this?

A restaurant sells steak meals for $20 and chicken meals for $15. If 30 meals total $500, what system represents this?

A farmer has $450 for 40 apple and lemon trees. Apple trees are $10, and lemons are $15. How many apple trees are there?

• 25 apple trees

• 20 apple trees

• 30 apple trees

• 15 apple trees

A shop sells 15 pairs of shoes for $930. Sneakers cost $50, and boots cost $80. How many sneakers are included?

• 6 sneakers

• 8 sneakers

• 9 sneakers

• 11 sneakers

100 tickets sold. Adult tickets are $10, and student tickets are $5. Total revenue is $700. What are the equations?

A bakery sells 50 cookies for $120. Chocolate cookies cost $2, and sugar cookies cost $3. What are the equations?

A gym sells memberships for $30 and $300. What is the first step to solve if 20 memberships sold for $3,600?

• Add the prices of the memberships

• Solve for monthly memberships

• Substitute values into the equations

• Set up equations for total memberships and cost