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.
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.
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
- 4th Grade ACT Aspire Math FREE Sample Practice Questions
- How to Prepare for the PSAT 10 Math Test?
- The Ultimate CLEP College Algebra Course (+FREE Worksheets & Tests)
- How to Solve Word Problems on Dividing Whole Numbers by Unit Fractions
- 5th Grade STAAR Math Worksheets: FREE & Printable
- How to Write the Equation of a Cosine Graph?
- A Deep Dive into the Chapters of the Book: Pre-Algebra for Beginners
- Billionaire Basics: How to Master Addition and Subtraction of Massive Whole Numbers
- Line Segments
- A Comprehensive Collection of Free ALEKS Math Practice Tests
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.