/*! 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 7 An equation of the form \(A x+B ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 1: Problem 7

An equation of the form \(A x+B y=C\) is a _____ in two variables.

Short Answer

Expert verified
Linear equation

Step by step solution

01

Understanding the Equation

The given equation is in the form of \(Ax + By = C\), where \(A\), \(B\), and \(C\) are constants, and \(x\) and \(y\) are variables.
02

Identify the Form of the Equation

Equations of the form \(Ax + By = C\) are known as linear equations because they represent a straight line when plotted on a graph.
03

Determine the Type

Since the equation \(Ax + By = C\) represents a straight line, it is called a linear equation in two 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!

Key Concepts

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

Linear Equations in Two Variables
A linear equation in two variables is any equation that can be written in the form ax + by = c
Here,
  • . a, b, and c are constants
  • x and y are variables.

This equation represents a straight line in a 2D coordinate system.


When both variables are at power one, this equation is linear and we can expect it to graph as a straight line.

To illustrate, consider the example equation: 3x - 2y = 5.
Here, 3 and -2 are constants for x and y, respectively, and 5 is the constant term. As you can see, it matches the format Ax + By = C.
Graphing Linear Equations
Graphing linear equations is about taking a linear equation and plotting it on a coordinate plane to see its visual representation. The graph of a linear equation in two variables is always a straight line.

To graph a linear equation:
  • 1. Find at least two points that satisfy the equation.
  • 2. Plot these points on the coordinate plane.
  • 3. Draw a line through these points.
For instance, let's graph the equation 2x + 3y = 6. By substituting values of x, we can calculate corresponding values of y to find points. When x=0, y=2 and when x=3, y=0. Plot these points and draw a straight line through them. That's how you visualize the linear equation!
Constants and Variables in Equations
In any linear equation, constants and variables play a key role:
  • Constants are fixed values. In the equation Ax + By = C, A, B, and C are constants. They define the slope and position of the line on the graph.
  • Variables are symbolic representations of values that can change. In Ax + By = C, x and y are variables.


Constants determine how steep your line is (slope) and where it crosses the y-axis (y-intercept). Variables indicate the points through which this line passes. Using our previous example, 2x + 3y = 6:
Here, 2 and 3 are the constants, while x and y are variables. By choosing different values of x, you calculate corresponding y values to find points that lie on your line.
Understanding the distinction between constants and variables is fundamental to mastering linear equations.

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 an exact solution to each problem. If the solution is irrational, then find an approximate solution also. Mixing Antifreeze in a Radiator Steve's car had a large radiator that contained an unknown amount of pure water. He added two quarts of antifrecze to the radiator. After testing, he decided that the percentage of antifreeze in the radiator was not large enough. Not knowing how to solve mixture problems, Steve decided to add one quart of water and another quart of antifreeze to the radiator to see what he would get. After testing he found that the last addition increased the percentage of antifreeze by three percentage points. How much water did the radiator contain originally?

Find the equation of the line (in standard form) through \((3,-4)\) that is perpendicular to \(2 x-y=1\).

Find the equation (in standard form) of the line through \((-2,6)\) that is parallel to \(4 x-5 y=8\) Find the product \((3-2 i)(3+2 i)\)

Solve each equation. $$\frac{3}{x}-\frac{4}{1-x}=\frac{7 x-3}{x^{2}-x}$$

Find an exact solution to each problem. If the solution is irrational, then find an approximate solution also. Use the linear regression feature of a graphing calculator to find the equation of the regression line for the points \((-2,1),(-1,2),(0,5),(1,4),\) and \((2,4)\)
See all solutions

Recommended explanations on Math Textbooks

Decision Maths

Read Explanation

Probability and Statistics

Read Explanation

Statistics

Read Explanation

Calculus

Read Explanation

Logic and Functions

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.