Mathematics
Grade 8
15 min
Solve word problems involving two-variable equations
Solve word problems involving two-variable equations
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1
Introduction & Learning Objectives
Learning Objectives
Identify unknown quantities in word problems and assign appropriate variables.
Translate verbal descriptions and relationships into two-variable linear equations.
Formulate a system of two linear equations from a given word problem.
Solve systems of two-variable linear equations using the substitution or elimination method.
Interpret the solution of a system of equations in the context of the original word problem.
Check the reasonableness and accuracy of their solutions.
Ever wonder how mathematicians solve real-life puzzles like figuring out how many apples and bananas you can buy with a certain amount of money? 🍎🍌
In this lesson, you'll learn how to transform everyday situations into mathematical equations with two unknown values. This skill is...
2
Key Concepts & Vocabulary
TermDefinitionExample
VariableA symbol, usually a letter (like 'x' or 'y'), that represents an unknown quantity or a value that can change.In the problem 'Let x be the number of apples,' 'x' is the variable representing the unknown count of apples.
Two-Variable EquationAn equation that contains two different variables, typically representing two distinct unknown quantities, and shows a relationship between them.The equation `2x + 3y = 10` is a two-variable equation, where 'x' and 'y' are the variables.
Word ProblemA mathematical problem presented in a narrative or descriptive form, requiring you to translate the given information into mathematical expressions and equations to find a solution.''The sum of two numbers is...
3
Core Formulas
Rule 1: Translating Verbal Phrases to Algebraic Expressions
Identify keywords (e.g., 'sum', 'difference', 'product', 'quotient', 'is', 'more than', 'less than') and convert them into corresponding mathematical operations and equality signs.
This rule is the foundation for converting the narrative of a word problem into a mathematical equation. For instance, 'is' typically means '=', 'sum' means '+', 'product' means '×', 'more than' means '+', and 'less than' means '-' (with careful attention to order).
Rule 2: Setting Up Two-Variable Equations from Word Problems
1. Read the problem carefully to understand the...
4 more steps in this tutorial
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Easy
According to the tutorial, what is the very first step you should take when solving a word problem involving two unknown quantities?
A.Choose whether to use substitution or elimination.
B.Write two equations based on the information.
C.Identify the unknown quantities and assign a distinct variable to each.
D.Solve the system of equations for x and y.
Easy
Which phrase from a word problem is correctly translated into the equation `x + y = 20`?
A.The product of two numbers is 20.
B.The sum of two numbers is 20.
C.The difference between two numbers is 20.
D.One number is 20 more than the other.
Easy
Based on the tutorial's 'Common Pitfalls to Avoid' section, which of the following is an example of an INCORRECT or vague variable definition?
A.Let a = the number of adult tickets sold.
B.Let c = the number of child tickets sold.
C.Let x = tickets.
D.Let p = the price of one pizza in dollars.
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