# Deriving Equations

## The Significance of Solving Equations

When studying GCSE mathematics, you may encounter various equations to solve. But why is this important? The main purpose of solving equations is to determine the value of an unknown quantity. This unknown quantity is usually represented by a variable, such as x or y, which can represent anything from the cost of apples to an unknown angle in a shape. In this article, we will not only explore the process of solving equations but also showcase the usefulness of creating and solving equations. This process of creating an equation is known as deriving.

## Understanding the Concept of Deriving Equations

While we often solve equations, it is crucial to understand what an equation truly is. Breaking down the word "equation," we get "equa" and "tion." "Equa" is similar to "equal," which is fitting because an equation is essentially anything with an equal sign. It is a statement of equality between two variables. Therefore, when faced with a question involving the equality of variables, we can form and solve an equation.

## Defining Variables

A variable is a letter or symbol that represents an unknown value. We typically use x and y for variables, but it can be any letter or symbol. To derive an equation, we must first define any unknown variables to establish what we are trying to solve for. For instance, if a question asks for a person's age, we can define their age as a. Similarly, if the question involves the cost of an item, we can define the cost as c or any other variable.

## Methods for Deriving Equations

To derive an equation, we can follow a few simple steps:

• Define Variables: As mentioned earlier, start by defining any unknown variables to determine what you are trying to solve for.
• Identify Equal Quantities: Next, determine where the equals sign should go. Sometimes, this may be explicitly stated in the question, but other times you may need to use your knowledge. For example, if three unknown angles are on a straight line, their sum is 180 degrees. Therefore, we can use this information to form an equation. Similarly, if we have a square or rectangle, we know that the parallel sides are equal, making it useful for deriving equations.

## Examples of Deriving Equations

Let's practice deriving equations with some examples.

### Finding Missing Angles

Given the following straight line, what is the value of angle DBC?

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