/*! 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 49 Describe in general terms how to... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 4: Problem 49

Describe in general terms how to solve a system in three variables.

Short Answer

Expert verified
To solve a system in three variables, set up the equations first. Next, eliminate one variable from two sets of equations to create two equations with two variables each. Solve this system to get the values of two variables. Substitute these values back into one of the original equations to find the value of the third variable.

Step by step solution

01

Set Up the Equations

Write down the system of three equations. To be able to solve for three variables, you need at least three different equations. The equations should represent a mathematical model of the problem you're trying to solve.
02

Eliminate One Variable from Two of the Equations

Pick two equations and eliminate one variable by adding, subtracting, or multiplying the equations. This will give you a new equation with only two variables.
03

Create Another Two Variable Equation

Pick another pair of equations (at least one of which hasn't been used in Step 2) and eliminate the same variable as in Step 2. This will give you a second equation with two variables.
04

Find a Solution for the Two-Variable System

Now, you have a system of two equations with two variables. Solve this system using substitution or elimination, which gives you the value for two of the variables.
05

Solve for the Third Variable

Substitute the two found variables into one of the original equations. Solve for the third variable. Now you have the solution for all three variables.

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

Solve each system or state that the system is inconsistent or dependent. $$\left\\{\begin{array}{l}0.4 x+y=2.2 \\ 0.5 x-1.2 y=0.3\end{array}\right.$$

Things did not go quite as planned. You invested \(\$ 30,000\) part of it in a stock with a \(14 \%\) annual return. However the rest of the money suffered a \(6 \%\) loss. If the total annual income from both investments was \(\$ 200,\) how much was invested at each rate?

When using the substitution method, how can you tell if a system of linear equations has no solution?

A jeweler needs to mix an alloy with a \(16 \%\) gold content and an alloy with a \(28 \%\) gold content to obtain 32 ounces of a new alloy with a \(25 \%\) gold content. How many ounces of each of the original alloys must be used?

Solve each system or state that the system is inconsistent or dependent. $$\left\\{\begin{array}{l}5(x+1)=7(y+1)-7 \\\ 6(x+1)+5=5(y+1)\end{array}\right.$$
See all solutions

Recommended explanations on Math Textbooks

Pure Maths

Read Explanation

Calculus

Read Explanation

Applied Mathematics

Read Explanation

Probability and Statistics

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Decision 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.