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Understanding Variables and Constants

The Building Blocks of Equations

Think of an equation as a sentence. Just like sentences have nouns and verbs, equations have their own special parts that help us describe relationships between numbers. The two most basic parts are variables and constants.

A variable is a symbol, usually a letter like xx or yy, that stands in for a number we don't know yet. It's a placeholder for a value that can change or that we need to figure out. Imagine you have a box, but you don't know how many apples are inside. You could use the letter aa to represent the unknown number of apples.

Variable

noun

A symbol, typically a letter, used to represent an unknown or changing quantity in a mathematical expression.

Variables are the mysteries of algebra. Our goal is often to find out what number they're hiding.

The Unchanging Numbers

If variables are the unknowns, constants are the parts we do know. A constant is a number whose value is fixed and doesn't change within a problem. In the sentence "I have 2 hands and some number of fingers," the number 2 is a constant. It's a fact. The number of fingers could be a variable if we didn't know it, but the number of hands is fixed.

Constant

noun

A value in a mathematical expression that does not change.

So, if you see an equation like y=3x8y = 3x - 8, the numbers 3 and -8 are constants. Their values are set. The letters xx and yy are variables because their values can change depending on the situation.

Putting It All Together

Variables and constants work together to form mathematical expressions and equations. Let's look at a common scenario. Imagine you buy a cup of coffee for $3 and a few donuts that each cost $2. The total cost depends on how many donuts you buy.

We can represent this situation with an expression. Let's use the variable dd to stand for the number of donuts. The cost of the donuts would be 2d2d. Since the coffee is always $3, the total cost would be:

2d+32d + 3

In this expression, dd is the variable, while 2 and 3 are constants. The number 2, which is multiplied by the variable, has a special name: a coefficient. It tells us how many of the variable we have.

PartExampleRole
VariableddRepresents the unknown number of donuts.
Coefficient22The constant multiplied by the variable.
Constant33A fixed value, the cost of the coffee.

Soon, you'll be working with problems that have two different variables, known as a system of linear equations with two variables.

二元一次方程

Linear equation with two variables

This just means you'll have two mysteries to solve at once, using two variables like xx and yy. But the basic building blocks remain the same: variables represent the unknowns, and constants provide the fixed numbers you work with.

Quiz Questions 1/5

In the equation y=4x9y = 4x - 9, what does the letter 'x' represent?

Quiz Questions 2/5

A constant is a value in an equation that is always known and does not change.