Problem 39 Solve each formula for the indic... [FREE SOLUTION]

Chapter 2: Problem 39

Solve each formula for the indicated letter. $$ 9 x+8 y=4, \text { for } y $$

Short Answer

Expert verified

y = \frac{4 - 9x}{8}

Step by step solution

Isolate the y-term

The given equation is \[ 9x + 8y = 4 \]To solve for y, start by isolating the term that contains y. Subtract 9x from both sides of the equation.\[ 8y = 4 - 9x \]

Solve for y

Now, divide both sides of the equation by 8 to solve for y.\[ y = \frac{4 - 9x}{8} \]

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Key Concepts

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

Isolate the Variable

One of the fundamental concepts when solving linear equations is isolating the variable. This means you want to get the variable you are solving for by itself on one side of the equation.
To achieve this:

Identify the term with the variable.
Move all other terms to the opposite side by performing inverse operations, like addition and subtraction.

For instance, in the equation \[ 9x + 8y = 4 \], we isolate the y-term by subtracting 9x from both sides. This helps to separate y from the other terms in the equation.
Doing this step makes it much easier to solve for the target variable.

Algebraic Manipulation

Algebraic manipulation involves reorganizing and simplifying an equation to make it easier to solve.
Common techniques include:

Adding or subtracting terms on both sides.
Multiplying or dividing both sides by the same number.

In our example, after isolating the y-term to get \[ 8y = 4 - 9x \], the next step is to solve for y by dividing each term by 8.
Remember that whatever you do to one side of the equation, you must do to the other side. This maintains the balance of the equation, ensuring it remains true.
This results in \[ y = \frac{4 - 9x}{8} \], which gives us y in terms of x.

Understanding Linear Equations

A linear equation is an equation that represents a straight line when graphed on a coordinate plane. It typically takes the form of \[ ax + by = c \], where x and y are variables and a, b, and c are constants.
Key characteristics include:

They graph as straight lines.
They have a constant rate of change or slope.
They can be solved for any variable to express one variable in terms of the other.

Linear equations are foundational in algebra because they model many real-world scenarios. Understanding how to manipulate and solve these equations is critical for progressing in math.
In our problem, recognizing \[ 9x + 8y = 4 \] as a linear equation helps us understand that we are dealing with a straight-line relationship between x and y.

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91影视

Solve each formula for the indicated letter. $$ 9 x+8 y=4, \text { for } y $$

Short Answer

Step by step solution

Isolate the y-term

Solve for y

Key Concepts

Isolate the Variable

Algebraic Manipulation

Understanding Linear Equations

One App. One Place for Learning.

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