/*! 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 44 Explain how to solve a system of... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 4: Problem 44

Explain how to solve a system of equations using the substitution method. Use \(y=3-3 x\) and \(3 x+4 y=6\) to illustrate your explanation.

Short Answer

Expert verified
The solution to the system of equations is \(x=2/3\) and \(y=1\).

Step by step solution

01

Express One Variable in Terms of the Other

The first equation, \(y=3-3 x\), already expresses y in terms of x. Thus, \(y\) is equivalent to \(3-3 x\).
02

Substitute for the Variable in the Other Equation

Substitute \(3 - 3x\) for \(y\) in the second equation, resulting in \(3 x+4 (3-3 x)=6.\)
03

Simplify and Solve for the Variable

On simplifying the equation, it results in \(-9x + 12 = 6\). Solving for \(x\), yields the value \(x=2/3\).
04

Substituting x into the First Equation

Substitute \(x=2/3\) into the first equation \(y=3-3 x\). This results in \(y=3 - 3(2/3)\), which simplifies to \(y=1\).

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!

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

Find the value of \(m\) that makes $$\left\\{\begin{array}{l}y=m x+3 \\\5 x-2 y=7\end{array}\right.$$ an inconsistent system.

Write the slope-intercept form of the equation of the Tine passing through \((-5,6)\) and \((3,-10)\)

In Exercises \(45-56,\) solve each system by the method of your choice. If there is no solution or an infinite number of solutions, so state. Use set notation to express solution sets. Explain why you selected one method over the other two. $$\left\\{\begin{array}{l} 3 x+2 y=-3 \\ 2 x-5 y=17 \end{array}\right.$$

Involve mixtures How many ounces of a \(50 \%\) alcohol solution must be mixed with 80 ounces of a \(20 \%\) alcohol solution to make a \(40 \%\) alcohol solution?

In Exercises \(57-60\), write a system of equations modeling the given conditions. Then solve the system by the addition method and find the two numbers. Three times a first number increased by twice a second number is \(11 .\) The difference between the first number and twice the second number is 9. Find the numbers.
See all solutions

Recommended explanations on Math Textbooks

Statistics

Read Explanation

Logic and Functions

Read Explanation

Mechanics Maths

Read Explanation

Probability and Statistics

Read Explanation

Decision 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.