Understanding how to solve linear equations is one of the first big steps in learning algebra. It’s a skill every student need, whether you’re working through school assignments or brushing up on math after a break. Once you get the hang of it, solving these equations feels simple and useful — especially when you see how often they show up in real-life situations.
At allassignmenthelp.org, we believe math doesn’t have to be confusing. That’s why we break down tough topics like linear equations into clear, easy steps. In this guide, we’ll walk you through how to solve linear equations using real examples, everyday problems, and simple methods that actually work.
What Are Linear Equations?
A linear equation is a type of algebraic equation where the highest power of the variable is 1. It can have one or two variables and looks something like this:
- One-variable: 2x + 5 = 11
- Two-variable: x + y = 7
These equations form straight lines when drawn on a graph, which is why they are called “linear”.
Why Are Linear Equations Important?
Linear equations are used everywhere. From budgeting money to calculating distance or planning a trip, they play a role in everyday decisions. They also form the base for more advanced topics like calculus and statistics. If you’re a student, mastering this topic will help you with assignments, exams, and problem-solving tasks.
Key Terms to Know
Before we begin solving, let’s cover some simple terms:
- Variable: A letter (like x or y) that stands for a number
- Coefficient: The number in front of the variable (e.g., in 3x, 3 is the coefficient)
- Constant: A number on its own (e.g., in x + 2 = 5, 2 and 5 are constants)
- Equation: A statement showing two sides are equal
Rules of Solving Algebraic Equations
To solve equations correctly, remember these basic rules:
- Keep both sides of the equation balanced.
- Whatever you do on one side, do the same on the other.
- Use inverse operations (like adding to cancel out subtraction).
Simplifying Linear Equations Step by Step
Let’s break it down:
Step 1: Remove brackets if any
Example: 2(x + 3) = 12
Solution: Multiply to remove brackets: 2x + 6 = 12
Step 2: Combine like terms
Example: 3x + 2x = 10
Solution: 5x = 10
Step 3: Move constants to the other side
Example: x + 5 = 9
Solution: Subtract 5: x = 4
Step 4: Divide to isolate the variable
Example: 4x = 20
Solution: Divide by 4: x = 5
These steps apply to one-variable equations.
Solving Linear Equations With Two Variables
When you see equations like:
x + y = 10
x – y = 2
You need a method to solve them. Let’s look at the most common ones:
- Substitution Method
Solve one equation for one variable, then plug that into the second.
Example:
x = y + 2
x + y = 10
Substitute: (y + 2) + y = 10 → 2y + 2 = 10 → y = 4
Then, x = 6
- Elimination Method
Add or subtract equations to eliminate one variable.
Example:
2x + y = 8
x – y = 1
Add them: 3x = 9 → x = 3, then y = 2
- Graphical Method of Solving Equations
Plot both equations on a graph. The point where the lines cross is the solution.
This method helps visual learners and works well when both equations are simple.
Linear Equations in Real Life Examples
- Shopping: You buy two pens and three pencils. The total cost is AU$6. A pen is AU$1 each. Set up a linear equation to find the pencil’s price.
- Travel: A train moves at 60 km/h and travels 300 km. Find the time using the equation: Speed x Time = Distance.
- Budgeting: You earn AU$15 per hour and want to make AU$60. Use the equation: 15x = 60
These are all word problems with linear equations that can be solved using the methods above.
Common Mistakes When Solving Linear Equations
Avoid these errors:
- Forgetting to apply the same operation to both sides
- Mixing up negative signs
- Skipping simplification
- Incorrectly using the substitution method or elimination method in algebra
Always double-check your steps.
Tips to Master Solving Linear Equations
- Practise daily with different types of questions
- Start with easy problems, then move to complex ones
- Use the equation balancing method carefully
- Solve linear equations using substitution method when equations are already solved for one variable
- Use the elimination method in algebra for symmetrical coefficients
Final Thoughts
Learning how to solve linear equations doesn’t have to be tough. With regular practice, a clear understanding of rules, and step-by-step problem solving, anyone can master it. Whether you’re working on algebra basics or preparing for an assignment, these methods will guide you.
At allassignmenthelp.org, we support students across Australia with personalised assignment help. If you’re stuck with maths problems or need help with algebra topics, our experts are here to assist. Our work is always accurate, plagiarism-free, and tailored for your academic success.
Read more: How to Solve a Variable Equation
Frequently Asked Questions (FAQs)
What is the easiest way to solve linear equations?
The easiest way is to follow four simple steps: remove brackets, combine like terms, move constants to the other side, and isolate the variable. Start with one-variable equations before trying harder ones.
How do I solve linear equations with two variables?
You can use the substitution method, elimination method, or graph method. Substitution is best when one variable is already isolated. Elimination works well when both equations are in standard form. Graphing is useful for quick checks.
Why are linear equations used in real life?
Linear equations help solve everyday problems. You can use them to plan budgets, calculate travel time, or compare prices. They make maths useful and practical in daily life.
