## The Definition

of a Virtual Machine

A virtual machine is a software program that enables a computer to behave as if it were another separate computer. It allows a single physical computer to run multiple separate operating systems and applications concurrently.

## Pairs of Linear Equations in Two Variables

A pair of linear equations in two variables is a set of two equations in two variables that are consistent, which means that they have the same solutions. The equations are written in standard form, which is Ax + By = C.

To solve a pair of linear equations in two variables, you can use the following steps:

1. Solve one of the equations for one of the variables.

2. Substitute the value of the variable from the first equation into the other equation.

3. Solve the equation for the variable.

4. Check your solution.

Here is an example of how to solve a pair of linear equations in two variables:

x + 2y = 3

3x – 2y = 5

Solve the first equation for x.

x = 3 – 2y

Substitute 3 – 2y for x in the second equation.

3x – 2y = 5

3x – 2(3 – 2y) = 5

3x – 6y = 5

Solve the equation for y.

y = 5 – 3x

Check your solution.

x + 2y = 3

3x – 2y = 5

3x – 2(5 – 3x) = 5

3x – 2x = 5

The solutions to the pair of linear equations are

## Linear Equation in Two Variables Definition

A linear equation in two variables is an equation of the form

ax + by = c

where a, b, and c are real numbers. The equation represents a line in the plane with slope a and y-intercept b.

## Linear Equations in Variables

Ax + By = C

A straight line can be represented by the equation y = mx + b, where m is the slope and b is the y-intercept.

## Linear Equation in Two Variable Formula

A linear equation in two variable is a mathematical equation in which each variable is represented by a single letter and the equation consists of a linear combination of these variables with a constant term.

The general form of a linear equation in two variable is:

ax + by = c

Where a, b and c are constants.

## Solving Linear Equations in Two Variables

A linear equation in two variables is an equation of the form

ax + by = c

where a, b, and c are real numbers and x and y are variables.

There are three methods for solving linear equations in two variables:

1. Substitution

2. Elimination

3. Graphical methods

The following examples will illustrate how to solve linear equations in two variables using each of these methods.

Example 1: Solve the equation 3x + 2y = 10 for y.

Solution:

1. Substitution: y = 10 – 3x

2. Elimination: Add 3x to both sides of the equation:

3x + 2y = 10

3x + 3x + 2y = 10

2y = 10

y = 5

3. Graphical methods

## Plotting Graph of Linear Equations in Two Variables

The graph of a linear equation in two variables is a line. The equation of the line can be written in slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept. The slope of the line is the change in y divided by the change in x. The y-intercept is the point at which the line intersects the y-axis.

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## Problems and Solutions

Problem

How can I keep my computer from going to sleep?

Solution

There are a few ways to keep your computer from going to sleep. One is to change the settings in the Power Options section of the Control Panel. Another is to use a program like caffeine to keep your computer from going to sleep.