# How to Solve Systems of Equations Word Problems

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.

### Systems of Equations Word Problems – 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?

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 for Solving Systems of Equations Word Problems

### 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.

• There are $$8$$ pigs and $$2$$ ducks.
• There are $$3$$ cars and $$4$$ buses.
• $$10$$ and $$4$$.
• $$34$$.
• $$24$$ and $$42$$.

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