Linear Equations Applications Problems with Systems of Equations

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?

Solve the system. 

• (5, -6, 3)

• (2, 3, -1)

• (-4, 2, 5)

• No Solution

Solve the system.

• (2, -2, 3)

• (2, 1, 4)

• (-2, 2, -3)

• No Solution

Solve the system.

• (1, 2, -2)

• (1, -3, -2)

• (-1, 3, 2)

• No Solution

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

Solve for x and y
3x + 2y = 16
7x + y = 19

• (-2,5)

• (-2,-5)

• (2,-5)

• (2,5)