2.6 Solve a formula for a specific variable  (Page 3/4)

Later in this class, and in future algebra classes, you’ll encounter equations that relate two variables, usually x and y . You might be given an equation that is solved for y and need to solve it for x , or vice versa. In the following example, we’re given an equation with both x and y on the same side and we’ll solve it for y .

Solve the formula $3x+2y=18$ for y :

ⓐ when $x=4$ ⓑ in general

Solution

ⓐ when $x=4$			ⓑ in general
Substitute.
Subtract to isolate the $y$ -term.				Subtract to isolate the $y$ -term.
Divide.				Divide.
Simplify.				Simplify.

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In Examples 1.60 through 1.64 we used the numbers in part ⓐ as a guide to solving in general in part ⓑ . Now we will solve a formula in general without using numbers as a guide.

Solve the formula $P=a+b+c$ for $a$ .

Solution

We will isolate $a$ on one side of the equation.
Both $b$ and $c$ are added to $a$ , so we subtract them from both sides of the equation.
Simplify.

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Solve the formula $6x+5y=13$ for y.

Solution

Subtract $6x$ from both sides to isolate the term with $y$ .
Simplify.
Divide by 5 to make the coefficient 1.
Simplify.

The fraction is simplified. We cannot divide $13-6x$ by 5.

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Key concepts

• To Solve an Application (with a formula)
  1. Read the problem. Make sure all the words and ideas are understood.
  2. Identify what we are looking for.
  3. Name what we are looking for. Choose a variable to represent that quantity.
  4. Translate into an equation. Write the appropriate formula for the situation. Substitute in the given information.
  5. Solve the equation using good algebra techniques.
  6. Check the answer in the problem and make sure it makes sense.
  7. Answer the question with a complete sentence.
• Distance, Rate and Time
  For an object moving at a uniform (constant) rate, the distance traveled, the elapsed time, and the rate are related by the formula: $d=rt$ where d = distance, r = rate, t = time.
• To solve a formula for a specific variable means to get that variable by itself with a coefficient of 1 on one side of the equation and all other variables and constants on the other side.

Practice makes perfect

Use the Distance, Rate, and Time Formula

In the following exercises, solve.