How to Solve Systems of Equations Word Problems? (+FREE Worksheet!)
Learn how to create and solve systems of equations word problems by the elimination method.
[include_netrun_products_block from-products="product/ged-math-test-prep-in-30-days-complete-study-guide-and-test-tutor-for-ged-mathematics-the-ultimate-book-for-beginners-and-pros-two-practice-tests/" product-list-class="bundle-products float-left" product-item-class="float-left" product-item-image-container-class="p-0 float-left" product-item-image-container-size="col-2" product-item-image-container-custom-style="" product-item-container-size="" product-item-add-to-cart-class="btn-accent btn-purchase-ajax" product-item-button-custom-url="{{url}}/?ajax-add-to-cart={{id}}" product-item-button-custom-url-if-not-salable="{{productUrl}} product-item-container-class="" product-item-element-order="image,title,purchase,price" product-item-title-size="" product-item-title-wrapper-size="col-10" product-item-title-tag="h3" product-item-title-class="mt-0" product-item-title-wrapper-class="float-left pr-0" product-item-price-size="" product-item-purchase-size="" product-item-purchase-wrapper-size="" product-item-price-wrapper-class="pr-0 float-left" product-item-price-wrapper-size="col-10" product-item-read-more-text="" product-item-add-to-cart-text="" product-item-add-to-cart-custom-attribute="title='Purchase this book with single click'" product-item-thumbnail-size="290-380" show-details="false" show-excerpt="false" paginate="false" lazy-load="true"]
Related Topics
- How to Solve One-Step Equations
- How to Solve One-Step Inequalities
- How to Solve Multi-Step Inequalities
- How to Solve Systems of Equations
- How to Graph Single–Variable Inequalities
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.
For education statistics and research National Center for Education Statistics.
The Absolute Perfect Practice Workbook for Algebra I
Systems of Equations Word Problems – Example 1:
Tickets to a movie cost \($8\) for adults and \($5\) for students. A group of friends purchased \(20\) tickets for \($115.00\). How many adult tickets 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 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 holds \(45\) 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 is 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 \(42\).
The Best Books to Ace Algebra
Related to This Article
More math articles
- Back to School: The Best Laptops for Students
- Classifying Triangles for 4th Grade
- Top 10 Math Books for Grade 6 Students: Inspiring Masterminds
- Number Properties Puzzle – Challenge 17
- 3rd Grade MEAP Math Practice Test Questions
- 10 Most Common 3rd Grade ACT Aspire Math Questions
- How to Solve Word Problems with Four-digit Dividends and Two-digit Divisors
- The Ultimate 6th Grade MCAP Math Course (+FREE Worksheets)
- FREE ASVAB Math Practice Test
- Do My Essay for Me: What Are the Benefits of Remote Learning?
What people say about "How to Solve Systems of Equations Word Problems? (+FREE Worksheet!) - Effortless Math: We Help Students Learn to LOVE Mathematics"?
No one replied yet.