Learn how to create and solve systems of equations word problems by elimination method.

## Step by step guide to solve systems of equations word Problems

- Find the key information in the word problem that can help you define the variables.
- Define two variables: \(x\) and \(y\)
- Write two equations.
- Use the elimination method for solving systems of equations.
- Check the solution by substituting the ordered pair into the original equations.

### Example:

Tickets to a movie cost \($8\) for adults and \($5\) for students. A group of friends purchased \(20\) tickets for \($115.00\). How many adults ticket did they buy?

**Answer:**

Let \(x\) be the number of adult tickets and \(y\) be the number of student tickets. There are \(20\) tickets. Then: \(x+y=20\). The cost of adults’ tickets is \($8\) and for students ticket is \($5\), and the total cost is \($115\). So, \(8x+5y=115\). Now, we have a system of equations: \(\begin{cases}x+y=20 \\ 8x+5y=115\end{cases}\)

Multiply the first equation by \(-5\) and add to the second equation: \(-5(x+y= 20)=- \ 5x-5y=- \ 100\)

\(8x+5y+(-5x-5y)=115-100→3x=15→x=5→5+y=20→y=15\). There are \(5\) adult tickets and \(15\) student tickets.

## Exercises

### Solve.

- A farmhouse shelters \(10\) animals, some are pigs and some are ducks. Altogether there are \(36\) legs. How many of each animal are there?
- A class of \(195\) students went on a field trip. They took vehicles, some cars and some buses. Find the number of cars and the number of buses they took if each car holds \(5\) students and each bus hold \(45\) students.
- The difference of two numbers is \(6\). Their sum is \(14\). Find the numbers.
- The sum of the digits of a certain two–digit number is \(7\). Reversing its increasing the number by \(9\). What is the number?
- The difference of two numbers is \(18\). Their sum is \(66\). Find the numbers.

### Download Systems of Equations Word Problems Worksheet

## Answers

- There are \(8\) pigs and \(2\) ducks.
- There are \(3\) cars and \(4\) buses.
- \(10\) and \(4\).
- \(34\).
- \(24\) and \(42\).