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Chapter 9: Problem 343

In the following exercises, solve. Solve the formula 8x + y = 15 for y.

Short Answer

Expert verified
y = 15 - 8x

Step by step solution

01

- Identify the original equation

The equation provided is:\[ 8x + y = 15 \]
02

- Isolate the variable y

To solve for \( y \), isolate it on one side of the equation. Subtract \( 8x \) from both sides of the equation:\[ y = 15 - 8x \]

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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 linear equations like the one given, you often need to isolate the variable you are solving for. Isolating the variable means getting the desired variable by itself on one side of the equation.
This process helps in understanding what value the variable holds.
For the equation given, we aim to solve for the variable 'y'. We need to have 'y' on one side of the equation and everything else on the other side.
This usually involves moving other terms across the equal sign by doing basic arithmetic operations such as addition, subtraction, multiplication, or division.
Solve for y
Our goal is to rewrite the equation so that 'y' stands alone on one side of the equation. We start with the given equation:
\[ 8x + y = 15 \]
To isolate 'y', we need to move '8x' to the other side. We do this by subtracting '8x' from both sides of the equation:
\[ 8x + y - 8x = 15 - 8x \]
This simplifies to:
\[ y = 15 - 8x \]
By following this approach, you now have 'y' isolated, making it easier to understand how 'y' varies with 'x'.
Algebraic Manipulation
Algebraic manipulation involves moving variables and constants around the equation to simplify it or solve for a particular variable. This process uses operations such as addition, subtraction, multiplication, and division.
In the given exercise, we needed to perform algebraic manipulation to isolate 'y'. By subtracting '8x' from both sides, we simplified the equation while keeping it balanced.
This is crucial because whatever you do to one side of the equation, you must do to the other side to maintain equality. This balance is the core principle behind solving equations in algebra.

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