/*! 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 48 Find \(y\) given that \(x=3\). ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 2: Problem 48

Find \(y\) given that \(x=3\). $$-x-3 y=6$$

Short Answer

Expert verified
y = -3

Step by step solution

01

Substitute the value of x

Given that \(x = 3\), substitute this value into the equation \-x - 3y = 6\. The equation becomes: \-3 - 3y = 6\.
02

Solve for y

First, isolate the term with \(y\) by adding 3 to both sides of the equation: \-3 - 3y + 3 = 6 + 3 \Rightarrow -3y = 9\. Next, divide both sides by -3 to solve for \(y\): \frac{-3y}{-3} = \frac{9}{-3}\ \Rightarrow y = -3\.

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.

substitution method
The substitution method is a way to solve linear equations by replacing one variable with its given value. In this exercise, we know that \(x\) is equal to 3. So, we substitute 3 wherever we see the variable \(x\) in the equation. This simplifies the equation, making it easier to solve for the other variable.
For example, the original equation \-x - 3y = 6\ turns into \-3 - 3y = 6\ when we substitute \(x = 3\). Now, we can move on to isolating the variable \(y\) and solve the simplified equation.
isolating variables
Isolating variables means getting one variable alone on one side of the equation. This helps us solve for that variable. In our example, after substitution, we have the equation: \-3 - 3y = 6\. To isolate \(y\), we need to remove the constant term on the left side.
We do this by adding 3 to both sides: \-3 - 3y + 3 = 6 + 3\. Simplifying, we get \-3y = 9\.
Now the variable \(y\) term is isolated. The next step is to solve for it by using algebraic manipulation.
algebraic manipulation
Algebraic manipulation involves basic operations such as addition, subtraction, multiplication, and division to solve for the variable. In our example, we have \-3y = 9\ after isolating \(y\).
To find \(y\), we'll divide both sides by -3:
\[ \frac{-3y}{-3} = \frac{9}{-3} \Rightarrow y = -3 \]
By dividing, we get \(y = -3\). Thus, solving linear equations often involves these steps of substitution, isolating variables, and algebraic manipulation to reach the solution.

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

Solve each equation. Practice combining some steps. Look for more efficient ways to solve each equation. $$1-3(x-2)=4(x-1)-3$$

Solve each problem. If the circumference of a circle is \(3 \pi\) meters, then what is the radius?

Show a complete solution to each problem. Cruising America. Suzic and Scott drive together for American Freight. One day Suzie averaged 54 mph and Scott averaged \(58 \mathrm{mph},\) but Scott drove for 3 more hours than Suzie. If together they drove 734 miles, then for how many hours did Scott drive?

Discussion For which real numbers m and n is each equation satisfied? a) \(|m-n|=| n-m\) b) \(|m n|=|m| \cdot|n|\) c) \(\left|\frac{m}{n}\right|=\frac{|m|}{|n|}\)

Solve each problem by using a compound inequality. See Example 12. Selling-price range. Renee wants to sell her car through a broker who charges a commission of \(10 \%\) of the selling price. The book value of the car is \(\$ 14,900,\) but Renee still owes \(\$ 13,104\) on it. Although the car is in only fair condition and will not sell for more than the book value, Renee must get enough to at least pay off the loan. What is the range of the selling price?
See all solutions

Recommended explanations on Math Textbooks

Calculus

Read Explanation

Applied Mathematics

Read Explanation

Geometry

Read Explanation

Statistics

Read Explanation

Mechanics Maths

Read Explanation

Pure Maths

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.