What is a linear equation in the context of Edexcel IGCSE Mathematics?

In Edexcel IGCSE Mathematics, a linear equation is an algebraic equation in which each term is either a constant or the product of a constant and a single variable. Linear equations are typically in the form of ax + b = 0, where 'a' and 'b' are constants, and 'x' is the variable. These equations graph as straight lines on a coordinate plane.

How do you solve a linear equation with one variable?

To solve a linear equation with one variable, you need to isolate the variable on one side of the equation. This can be done by performing operations such as addition, subtraction, multiplication, or division on both sides of the equation. For example, to solve 2x + 3 = 7, you would subtract 3 from both sides to get 2x = 4, and then divide both sides by 2 to find x = 2.

What are the steps to graph a linear equation on a coordinate plane?

To graph a linear equation on a coordinate plane, follow these steps: 1) Rewrite the equation in the form y = mx + c, where 'm' is the slope and 'c' is the y-intercept. 2) Plot the y-intercept on the y-axis. 3) Use the slope to determine another point on the line by rising and running from the y-intercept. 4) Draw a straight line through the points. This line represents the solutions to the equation.

What is the significance of the slope and y-intercept in a linear equation?

In a linear equation of the form y = mx + c, the slope 'm' represents the rate of change or the steepness of the line. It indicates how much 'y' changes for a unit change in 'x'. The y-intercept 'c' is the point where the line crosses the y-axis, representing the value of 'y' when 'x' is zero. Understanding these components helps in interpreting and graphing linear relationships.

How can linear equations be used to solve real-world problems?

Linear equations are used to model and solve real-world problems involving relationships between two quantities. For example, they can be used to calculate distances, predict financial outcomes, or determine rates of change. By setting up an equation based on the problem's conditions, you can solve for unknown variables and make informed decisions based on the results.

Equations, Formulae and IdentitiesEdexcel IGCSE Mathematics (4MA1)

Linear Equations

Work through the notes, try the practice questions, then take the quiz. The report tells you exactly what to revise next.

Previous Next

Notes & worked examples

Read the notes first. If the method in a worked example clicks, you're ready for the questions.

Page 1 / 0

Study Notes & Exam Tips

The shortest version of this sub-topic — plus the mistakes examiners mark you down for.

Study Notes

A linear equation is an equation where the highest degree of any variable is 1, and its graph forms a straight line. Solving linear equations involves finding the value of the variable that makes the equation true.

Linear Equation — an equation with the highest degree of 1.
Example: 8 - 10x = 6
Solving Linear Equations — finding the value of the variable that satisfies the equation.
Example: 3x + 6 = 105 leads to x = 33
Forming Linear Equations — creating an equation from a word problem.
Example: The sum of three consecutive odd numbers is 105, leading to x + (x+2) + (x+4) = 105

Exam Tips

Key Definitions to Remember

A linear equation has no variable with a power greater than one.
Solving an equation means finding the value of the variable.

Common Confusions

Forgetting to apply the same operation to both sides of the equation.
Misinterpreting word problems when forming equations.

Typical Exam Questions

What is a linear equation? An equation with the highest degree of 1.
Solve for x: 7(x + 2) = 4(x + 5)? x = 6
A rectangle of perimeter 74 cm is 7 cm longer than it is wide. What is the length of each side? Width = 15 cm, Length = 22 cm

What Examiners Usually Test

Ability to solve linear equations accurately.
Skill in forming equations from word problems.
Understanding of the properties of linear equations.

Practice questions

Exam-style questions with step-by-step worked solutions. Try one before checking the method.

AI-marked quiz

Get a report showing which sub-topics you've nailed and which ones still need work.

Video lesson

Short walkthrough of the concepts students most often get stuck on.

Now Playing

Linear Equations

Video Playlist