# Algebraic Expressions

# Evaluating Formulas by Substitution

As we mentioned, a formula has a dependent variable on one side and an expression involving the independent variable(s) on the other side. To evaluate a formula, we evaluate the expression containing the independent variable(s). The result is the value of the dependent variable. Ready, Miss Independent? Let's make you Miss Dependent.

### Sample Problem

Consider the formula *C* = 5*xy*. Find *C* if *x* = 2 and *y* = 3.

*C* is the dependent variable, and that will be our result. Now, how do we find its value? We evaluate the expression on the other side of the equals sign, 5*xy*, for *x* = 2 and *y* = 3. This step gives us *C* = 5(2)(3) = 30. We now know *C*'s value is 30. However, we don't know if that is in dollars or pesos—no getting excited just yet.

We can use geometric formulas to answer all sorts of questions. Like, "Why is the sky blue?" or "What makes birds sing?" or "Why does Julia Stiles have a career?" Still, more practically, it can help us solve something like the below...

### Sample Problem

Find the area of a square with side length 4 cm.

The area of a square is given by the formula *A* = *s*^{2}, where *A* is the area of the square and* s* is the length of a side. In this case, the length of a side is 4, and we substitute 4 for *s* and evaluate the area formula: *A* = (4)^{2} = 16 cm^{2}. We will now let r represent rock star, which is what we are for finding the area of this square.