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Real World: Solving Systems of Equations Word Problems

Real World: Solving Systems of Equations Word Problems

Also included in: Solving Systems of Equations Activity Bundle

Solving Systems of Equations from Word Problems Activity | Mystery Algebra 1

Solving Systems of Equations from Word Problems Activity | Mystery Algebra 1

Also included in: Systems of Equations Activity and Notes Bundle

Solving Systems of Equations Word Problems - Notes & Homework

Solving Systems of Equations Word Problems - Notes & Homework

Amazing Mathematics

Also included in: 8th Grade Math Bundle ~ All My 8th Grade Math Products at 1 Low Price

Writing and Solving Systems of Equations Word Problems Jumbo Task Cards

Writing and Solving Systems of Equations Word Problems Jumbo Task Cards

Algebra Accents

Also included in: Back to School Algebra 1 Curriculum | Math Task Cards Growing BUNDLE

Solving Systems of Equations: Word Problems (Bundle)

Solving Systems of Equations: Word Problems (Bundle)

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Solve Linear Systems Word Problems Relay Activity Algebra 1 | Digital

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Systems of Equations Word Problems | Solving Systems of Linear Equations

Systems of Equations Word Problems | Solving Systems of Linear Equations

$Make Sense of Math$

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$Solve Systems of Equations Given Word Problems Exam (Mrs Math)$

Solve Systems of Equations Given Word Problems Exam (Mrs Math)

$Mrs MATH$

Write & Solve Systems from Word Problems

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Solving Systems of Equations Word Problems (by Substitution)

Also included in: Solving Systems of Equations: Word Problems (Bundle)

Writing and Solving Systems of Equations from Word Problems Lesson

Writing and Solving Systems of Equations from Word Problems Lesson

$Math Beach Solutions$

Solve Linear Systems with Real World Word Problems Guided Practice Exit Ticket

Algebra Made Simple

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Gotta Solve 'em All: Metric System Word Problem Task Cards 4.MD.2

Gotta Solve 'em All: Metric System Word Problem Task Cards 4.MD.2

Solving Systems of Equations Word Problems Trivia Scavenger Hunt

Amusing Algebra

Also included in: Solving Two Variable Systems Activity Bundle

R.U.L.E.S. for Solving Systems of Equations Word Problems Powerpoint

R.U.L.E.S. for Solving Systems of Equations Word Problems Powerpoint

$Making Math Fun for All Learners$

Apply Systems of Equations Word Problems Solve & Flip

$Math Dyal$

Also included in: Systems Of Equations Bundle of Activities

Solving Systems Word Problems Practice

Solving Systems Word Problems Practice

$Secondary Math Solutions$

Also included in: Systems of Equations Unit Bundle - Algebra 1 Curriculum

Solving Systems of Equations Word Problems Coloring Activity

Solving Systems of Equations Word Problems Coloring Activity

HSA-BF.A.1 Algebra 1 Unit 2 Complete Lesson 13 Solve System of Eq Word Problems

HSA-BF.A.1 Algebra 1 Unit 2 Complete Lesson 13 Solve System of Eq Word Problems

$Math Created by the Dollar$

Setting Up Solving Systems of Equations Word Problems

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Using Systems to Solve Real-World Word Problems

Solving Systems of Linear Equations Word Problems Practice - Task Card Game

Also included in: Systems of Equations Word Problems - Notes, Practice & Activity SKILL BUNDLE

Solving Systems of Equations Given Word Problems Power Point 4-Lesson Pack

Solving Systems of Equations Given Word Problems Power Point 4-Lesson Pack

Solving Systems of Equations Word Problems Activity Differentiated Riddle

Solving Systems of Equations Word Problems Activity Differentiated Riddle

Organized in Algebra

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Solving Systems of Equations Word Problems Worksheets

We have previously learned about systems of equations. This is when you have multiple linear equations that have the same value for their unknown variables. this allows us to manipulate these equations in many different ways to determine those unknown variables. These systems are evident in many different real-world ways. Students will work with systems of equations that can be found within word problems in this problem set. The worksheets and lessons will show students how to setup up these problems and how to solve them.

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The quizzes were hard to get set correctly. It took me a while to get the numbers to balance.

What Are Systems of Equations in Math?

When you consider systems in mathematics, this normally refers to a series of linear equations that share the same values for their variables. Thus, we must learn the concepts of systems when we are learning algebra. Systems of the equation consist of at least two equations that have the same variables in them. In the concept, the number of equations is directly proportional to the number of variables present in them. Let us take an example which consists of variables x and y. You can communicate these types of problems in algebraic or narrative form.

There are number of different methods you can use to find the values of the variables within these systems. Here is an example of a system of equations: x + y = 6 and -3x + y = 2. Now, we need to solve them simultaneously, to get the values of x and y. When you solve them you will come across a condition. Let us resolve them. x = 6 - y : eq (a)| Here, we will place the value of x in the second equation. -3(6-y) + y = 2 unto -18 + 3y + y = 2 unto 4y = 18 + 2 unto y = 5. Now, we will place the value of y in eq (a). x = 6 - 5 therefore x = 1. The solution set is (1, 5). The condition is that on the graph, both lines will intersect at some point. Your goal by substituting values into the other equation is to locate this point. The best thing about this problem is that it easy to double check your solution. All you need to do is to plug the x and y value of your solution into both equations. If you are correct, they will work for both equations. For the purposes of this topic, we will focus on the narrative form with this topic, but to see it written algebraically is good to get us going.

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Solving Systems of Equations Real World Problems

Wow! You have learned many different strategies for solving systems of equations! First we started with Graphing Systems of Equations . Then we moved onto solving systems using the Substitution Method . In our last lesson we used the Linear Combinations or Addition Method to solve systems of equations.

Now we are ready to apply these strategies to solve real world problems! Are you ready? First let's look at some guidelines for solving real world problems and then we'll look at a few examples.

Steps For Solving Real World Problems

Ok... let's look at a few examples. Follow along with me. (Having a calculator will make it easier for you to follow along.)

Example 1: Systems Word Problems

You are running a concession stand at a basketball game. You are selling hot dogs and sodas. Each hot dog costs $1.50 and each soda costs $0.50. At the end of the night you made a total of $78.50. You sold a total of 87 hot dogs and sodas combined. You must report the number of hot dogs sold and the number of sodas sold. How many hot dogs were sold and how many sodas were sold?

1. Let's start by identifying the important information:

2. Define your variables.

Ask yourself, "What am I trying to solve for? What don't I know?

In this problem, I don't know how many hot dogs or sodas were sold. So this is what each variable will stand for. (Usually the question at the end will give you this information).

Let x = the number of hot dogs sold

Let y = the number of sodas sold

3. Write two equations.

One equation will be related to the price and one equation will be related to the quantity (or number) of hot dogs and sodas sold.

1.50x + 0.50y = 78.50 (Equation related to cost)

x + y = 87 (Equation related to the number sold)

We can choose any method that we like to solve the system of equations. I am going to choose the substitution method since I can easily solve the 2nd equation for y.

Solving a systems using substitution

5. Think about what this solution means.

x is the number of hot dogs and x = 35. That means that 35 hot dogs were sold.

y is the number of sodas and y = 52. That means that 52 sodas were sold.

6. Write your answer in a complete sentence.

35 hot dogs were sold and 52 sodas were sold.

7. Check your work by substituting.

1.50x + 0.50y = 78.50

1.50(35) + 0.50(52) = 78.50

52.50 + 26 = 78.50

Since both equations check properly, we know that our answers are correct!

That wasn't too bad, was it? The hardest part is writing the equations. From there you already know the strategies for solving. Think carefully about what's happening in the problem when trying to write the two equations.

Example 2: Another Word Problem

You and a friend go to Tacos Galore for lunch. You order three soft tacos and three burritos and your total bill is $11.25. Your friend's bill is $10.00 for four soft tacos and two burritos. How much do soft tacos cost? How much do burritos cost?

In this problem, I don't know the price of the soft tacos or the price of the burritos.

Let x = the price of 1 soft taco

Let y = the price of 1 burrito

One equation will be related your lunch and one equation will be related to your friend's lunch.

3x + 3y = 11.25 (Equation representing your lunch)

4x + 2y = 10 (Equation representing your friend's lunch)

We can choose any method that we like to solve the system of equations. I am going to choose the combinations method.

Solving Systems Using Combinations

5. Think about what the solution means in context of the problem.

x = the price of 1 soft taco and x = 1.25.

That means that 1 soft tacos costs $1.25.

y = the price of 1 burrito and y = 2.5.

That means that 1 burrito costs $2.50.

Yes, I know that word problems can be intimidating, but this is the whole reason why we are learning these skills. You must be able to apply your knowledge!

If you have difficulty with real world problems, you can find more examples and practice problems in the Algebra Class E-course.

Take a look at the questions that other students have submitted:

solving systems of equations word problems worksheet answer key with work

Problem about the WNBA

Systems problem about ages

Problem about milk consumption in the U.S.

Vans and Buses? How many rode in each?

Telephone Plans problem

Systems problem about hats and scarves

Apples and guavas please!

How much did Alice spend on shoes?

All about stamps

Going to the movies

Small pitchers and large pitchers - how much will they hold?

Chickens and dogs in the farm yard

solving systems of equations word problems worksheet answer key with work

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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.

How to Solve Systems of Equations Word Problems? (+FREE Worksheet!)

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Step by step guide to solve systems of equations word Problems

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 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

Download Systems of Equations Word Problems Worksheet

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Word Problems Worksheet 1 – This 6 problem algebra worksheet will help you practice creating and solving systems of equations to represent real-life situations. You will use the “ elimination ” method to eliminate variables from standard form equations. Word Problems Worksheet 1 RTF Word Problems Worksheet 1 PDF View Answers

Word Problems Worksheet 3 – This 6 problem algebra worksheet will help you practice creating and solving systems of equations to represent real-life situations. Most of the problems involve money, so make sure you’re ready for some decimals. Word Problems Worksheet 3 RTF Word Problems Worksheet 3 PDF View Answers

Word Problems Worksheet 4 – This 6 problem algebra worksheet will help you practice creating and solving systems of equations to represent real-life situations. Most of the problems involve money, and a few distractors are introduced. Word Problems Worksheet 4 RTF Word Problems Worksheet 4 PDF View Answers

Word Problems Worksheet 5 – This 8 problem algebra worksheet features more abstract word problems like “ The sum of x and y is 42. the difference of x and y is 13. Find x and y .” There are a few negative integers, so be careful! Word Problems Worksheet 5 RTF Word Problems Worksheet 5 PDF View Answers

Word Problems Worksheet 6 – This 8 problem algebra worksheet features more abstract word problems like “ The sum of twice a number, x, and twice another number, y, is 118. The value of y is one less than twice the value of x. Find x and y. ” One of the problems even has an infinite number of solutions! Word Problems Worksheet 6 RTF Word Problems Worksheet 6 PDF View Answers

These free systems of equations worksheets will help you practice solving real-life systems of equations using the “ elimination ” method. You will need to create and solve a system of equations to represent each situation. The exercises can also be solved using other algebraic methods if you choose.

This is a progressive series that starts simple with problems involving buying movie tickets and collecting for fundraisers. Eventually the negative numbers , decimals , the distributive property and “ the opposite of x ” come into play.

Each worksheet will help students master Common Core skills in the Algebra strand. They are great for ambitious students in pre-algebra or algebra classes.

These free elmination worksheets are printable and available in a variety of formats. Each sheet includes an example to help you get started. Of course, answer keys are provided as well.

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There are multiple problems with your worksheets. You have word problems which are unanswerable or answers which make no sense such as fractions of people. Your answer sheets are frequently incorrect. For a quick example: System of Equations- Word Problems #1 – KEY. Question #1 states that there are 9 tickets purchased, the Answer shows a=6 and b=2. 6+2 is 8 not 9. Question 5 on that same worksheet is unanswerable. I’ve found problems on worksheet 1, 2, 5 so far. How can you claim to have the best materials with so many clear problems?

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Work / Answers. Period: Solving systems of equations word problems worksheet. For all problems, define variables, write the system of equations and solve
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Real World: Solving Systems of Equations Word Problems ... the students to write the system, show their work, and give the answer.
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Solving Systems of Equations Word Problems Review. Name:_______KEY____________. 2. A television weighs 50 pounds and a microwave weighs 30 pounds.
Solving Systems of Equations Word Problems Worksheets
Students will work with systems of equations that can be found within word problems in this problem set. The worksheets and lessons will show students how
Solving Systems of Equations Word Problems
Solution · 1. Let's start by identifying the important information: hot dogs cost $1.50 · 2. Define your variables. Ask yourself, "What am I trying to solve for?
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