/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 98 Solve \(3 x+2 y=-8\) for \(y\).... [FREE SOLUTION] | 91影视

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Chapter 2: Problem 98

Solve \(3 x+2 y=-8\) for \(y\).

Short Answer

Expert verified
y = -4 - \frac{3x}{2}

Step by step solution

01

- Isolate the term with y

Start with the given equation: \(3x + 2y = -8\). Subtract \(3x\) from both sides to isolate the term with \(y\). This gives: \(2y = -8 - 3x\).
02

- Solve for y

Divide both sides of the equation by 2 to solve for \(y\). This results in: \(y = \frac{-8 - 3x}{2}\). Simplify the right-hand side: \(y = -4 - \frac{3x}{2}\).

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Key Concepts

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

headline of the respective core concept
Understanding how to solve linear equations involves a few essential steps, like isolating variables and rearranging terms. Let's break down these concepts to ensure you fully grasp them.
headline of the respective core concept
One primary skill in solving linear equations is isolating the variable. This often involves rearranging the equation to get the variable on one side by itself. In our given exercise, the goal is to solve for the variable 'y'. Start by isolating the term with y in the equation by performing inverse operations.

To isolate y in the equation, we start with:
\(3x + 2y = -8\).
By subtracting 3x from both sides, we move the x-term to the other side:
\(2y = -8 - 3x\).
This isolates the term involving y, making it easier to solve for y in the next steps.
headline of the respective core concept
Now that we've isolated the term containing y, it's time to solve for y. To do this, we need to perform arithmetic operations to get y on its own. From the equation:
\(2y = -8 - 3x\)
We divide both sides by 2 to isolate y completely:
\(y = \frac{-8 - 3x}{2}\)
This simplifies to:
\(y = -4 - \frac{3x}{2}\).
So, by dividing and simplifying, we have solved for y and expressed it in terms of x.
headline of the respective core concept
Linear equations, like the one in this exercise, involve variables raised to the power of one. These equations form straight lines when graphed. Understanding the structure of a linear equation is crucial for isolating variables and solving for specific terms.

A typical linear equation looks like:
\(Ax + By = C\)
where A, B, and C are constants.

In our example, 3 and 2 are constants (coefficients of x and y), and -8 is the constant on the other side. Linear equations can be rearranged and manipulated, as shown in the steps above, to find solutions for particular variables, making them fundamental in algebra and various fields of mathematics.

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Most popular questions from this chapter

For exercises 77-78, \(V=\frac{L W T}{144 \text { in. }^{3}}\) where \(V\) is the volume of lumber in board feet, \(L\) is the length, \(W\) is the width, and \(T\) is the thickness. The units of length, width, and thickness are inches. a. Solve \(V=\frac{L W T}{144 \text { in. }^{3}}\) for \(L\). Include the units of measurement. The thickness of each board in a pile is \(1.5\) in., and the width of each board is \(7.25 \mathrm{in}\). The volume of the boards is 348 board feet. Find the total length of the boards. .. Change this length into feet.

Monitoring or participating in social networks, texting, surfing the Internet, and using other technology can affect your concentration. You might need to limit multitasking to do effective studying. List the other tasks that you can manage at the same time that you are doing math homework or studying for a math test.

For exercises 37-52, (a) solve. (b) use a number line graph to represent the solution. (c) check the direction of the inequality sign. $$ -x+7 \leq-15 $$

Solve \(V=\frac{L W T}{144}\) for \(W\).

For exercises 37-52, (a) solve. (b) use a number line graph to represent the solution. (c) check the direction of the inequality sign. $$ 7 x+3<52 $$
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