Grade 8 Algebra Word Problems

How to solve algebra word problems using systems of linear equations?

Solving algebra word problems using systems of linear equations is a powerful technique when a problem involves two or more unknown quantities and provides multiple pieces of information (conditions) that relate these quantities.

The core idea is to translate each piece of information into a separate linear equation, creating a system of equations that can then be solved simultaneously.

• Systems of Equations Worksheets

  Printable
  Solve Systems of Equations with Substitution
  Solve Systems of Equations with Elimination
  Solve Systems of Equation Word Problems
  System of Equations using the Graphical Method
  System of Equations Word Problems using the Graphical Method
  System of Equations with No Solution
  

  Online
  Solve System of Equations by Substitution
  
  Solve System of Equations by Addition
  Solve System of Equations by Subtraction
  Solve System of Equations by Addition or Subtraction
  Solve by Multiplication and then Addition or Subtraction

General Steps to Solve Algebra Word Problems Using Systems of Linear Equations:
1. Read and Understand the Problem:
Read the entire problem carefully, multiple times if necessary.
Identify what the problem is asking you to find (the unknown quantities).
Identify all the given information and conditions.
2. Define Variables:
Assign a different variable to each of the unknown quantities you need to find.
Clearly write down what each variable represents.
3. Formulate the Equations:
Translate each distinct piece of information or relationship from the word problem into a separate linear equation.
You will typically need as many independent equations as you have variables. For two unknowns, you’ll need two equations.
4. Solve the System of Equations:
Use one of the following methods:
a) Substitution Method
b) Elimination Method
5. State the Answer:
Write your final answer clearly and completely, in the context of the original word problem, using appropriate units.

Videos

Grade 8 Algebra Word Problems
How to solve algebra word problems using systems of linear equations?

Example:
Devon is going to make 3 shelves for her father. He has a piece of lumber 12 feet long. She wants the top shelf to be half a foot shorter than the middle shelf, and the bottom shelf to be half a foot shorter than twice the length of the top shelf. How long will each shelf be if she uses the entire 12 feet of wood?

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Grade 8 Algebra Word Problems - Line Segments

Example:
If JK = 7x + 9, JL = 114 and KL = 9x + 9. Find KL.

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Grade 8 number word problems - common core
How to write word problems into systems of linear equations and solve systems of linear equations using elimination and substitution methods?

Example 1:
The sum of two numbers is 361 and the difference between the two numbers is 173. What are the two numbers?

Example 2:
There are 356 Grade 8 students at Euclid’s Middle School. Thirty-four more than four times the number of girls is equal to half the number of boys. How many boys are in Grade 8 at Euclid’s Middle School? How many girls?

Example 3:
A family member has some five-dollar bills and one-dollar bills in their wallet. Altogether she has 18 bills and a total of $62. How many of each bill does she have?

Example 1:
A friend bought 2 boxes of pencils and 8 notebooks for school and it cost him $11. He went back to the store the same day to buy school supplies for his younger brother. He spent $11.25 on 3 boxes of pencils and 5 notebooks. How much would notebooks cost?

Exercises:

1. A farm raises cows and chickens. The farmer has a total of 42 animals. One day he counts the legs of all of his animals and realizes he has a total of 114. How many cows does the farmer have? How many chickens?
2. The length of a rectangle is 4 times the width. The perimeter of the rectangle is 45 inches. What is the area of the rectangle?
3. The sum of the measures of angles x and y is 127". If the measure of angle x is 34° more than half the measure of angle y, what is the measure of each angle?

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