/*! 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 18 Solve each equation for \(y.\) ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 2: Problem 18

Solve each equation for \(y.\) $$ -5 x+3 y=12 $$

Short Answer

Expert verified
y = (5x + 12) / 3

Step by step solution

01

- Isolate the term with y

Start with the given equation: ewline ewline ewline ewline ewline ewline ewline\(-5x + 3y = 12\) ewline Add \(5x\) to both sides to isolate the term with y: ewline ewline ewline ewline ewline ewline ewline\(3y = 5x + 12\)
02

- Solve for y

Divide both sides of the equation by 3 to solve for y: ewline ewline ewline ewline \(y = \frac{5x + 12}{3}\) ewline ewline ewline ewline Now, you have y in terms of x.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

Key Concepts

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

linear equations
A linear equation is one of the most common types of equations in algebra. It's called 'linear' because it represents a straight line when graphed on a coordinate plane. Linear equations generally take the form:
\(ax + by = c\)
where \(a\), \(b\), and \(c\) are constants. The equation given in our problem:
\(-5x + 3y = 12\)
is indeed a linear equation. The main goal when solving linear equations is to find the value of one variable in terms of the other. This is usually done through techniques like isolating a variable and algebraic manipulation. Remember: Linear equations will never have variables raised to any power higher than 1.
isolating a variable
Isolating a variable is a crucial step in solving equations. It involves rearranging the equation so that one variable stands alone on one side of the equation. This often requires adding, subtracting, multiplying, or dividing terms from both sides of the equation. For instance, in the given problem:
\(-5x + 3y = 12\)
we need to isolate the term containing \(y\). To do this, we add \(5x\) to both sides:
\(3y = 5x + 12\).
Once the term with \(y\) is isolated, we can proceed to solving the equation by further simplifying. Isolating the variable makes it easier to see the relationship between the two variables.
algebraic manipulation
Algebraic manipulation involves using arithmetic operations to simplify and solve equations. It is essential for isolating variables and solving for unknowns. In our solution:
After isolating \(y\) with \(3y = 5x + 12\), we use algebraic manipulation to solve for \(y\).
We divide both sides of the equation by 3:
\(y = \frac{5x + 12}{3}\)
This step is crucial because it completes the process of solving for the variable. We now have \(y\) expressed in terms of \(x\). The ability to manipulate equations is a fundamental skill in algebra, useful in various mathematical and real-life applications.

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Let \(A=\\{1,2,3,4,5,6\\}, B=\\{1,3,5\\}, C=\\{1,6\\}\) and \(D=\\{4\\} .\) Specify each set. See Examples I and 5. $$ B \cup D $$

Jennifer Siegel invested some money at \(4.5 \%\) simple interest and \(\$ 1000\) less than twice this amount at \(3 \% .\) Her total annual income from the interest was \(\$ 1020 .\) How much was invested at each rate?

Let \(A=\\{1,2,3,4,5,6\\}, B=\\{1,3,5\\}, C=\\{1,6\\}\) and \(D=\\{4\\} .\) Specify each set. See Examples I and 5. $$ A \cap D $$

To solve a linear equation with decimals, we usually begin by multiplying by a power of 10 so that all coefficients are integers. What is the least power of 10 that will accomplish this goal in each equation? (a) \(0.05 x+0.12(x+5000)=940 \quad(\text { Exercise } 63)\) (b) \(0.006(x+2)=0.007 x+0.009 \quad \text { (Exercise } 69)\)

In baseball, winning percentage (Pct.) is commonly expressed as a decimal rounded to the nearest thousandth. To find the winning percentage of a team, divide the number of wins (W) by the total number of games played \((\mathrm{W}+\mathrm{L})\) Repeat Exercise 41 for the following standings for the Eastern Division of the National League. (a) Philadelphia (b) Atlanta (c) New York Mets (d) Washington $$ \begin{array}{|l|c|c|c|} \hline & {W} & {L} & {P c t} \\ \hline \text { Philadelphia } & {93} & {69} & {} \\ {\text { Florida }} & {87} & {75} & {.537} \\ {\text { Atlanta }} & {86} & {76} & {} \\ {\text { New York Mets }} & {70} & {92} \\ {\text { Washington }} & {59} & {103} \\ \hline \end{array} $$
See all solutions

Recommended explanations on Math Textbooks

Probability and Statistics

Read Explanation

Applied Mathematics

Read Explanation

Geometry

Read Explanation

Pure Maths

Read Explanation

Mechanics Maths

Read Explanation

Theoretical and Mathematical Physics

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.