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Chapter 9: Problem 344

In the following exercises, solve. Solve the formula 9x + y = 13 for y.

Short Answer

Expert verified
y = 13 - 9x.

Step by step solution

01

- Identify the given equation

The equation provided is: 9x + y = 13.
02

- Isolate the variable y

To solve for y, we need to isolate it on one side of the equation. Subtract 9x from both sides of the equation: 9x + y - 9x = 13 - 9x.
03

- Simplify the equation

Simplify the equation by combining like terms. This gives: y = 13 - 9x.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Isolate the Variable
To solve a linear equation, one of the most important steps is to isolate the variable you are solving for. In this problem, we need to find the value of y. This means we want y alone on one side of the equation.
Combine Like Terms
Combining like terms is essential when solving equations. In our equation 9x + y = 13, we notice that 9x is a term with x, whereas y is alone. Moving 9x to the other side requires us to do the opposite operation to balance the equation. We subtract 9x from both sides, giving us \[ 9x + y - 9x = 13 - 9x \] and leaving \[ y = 13 - 9x \]. Combining like terms simplifies the equation further.
Subtracting Expressions
Subtracting expressions helps move terms from one side of the equation to the other. In this problem, we applied subtraction to isolate the variable y. By subtracting 9x from both sides, we ensure that the equation remains balanced, which is a crucial rule in algebra. This operation helps us get the desired form, \[ y = 13 - 9x \], making it easier to extract the solution.

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