Identifying solutions to a linear equation in two variables calculator

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1. What are the popular methods to solve linear equations with two variables?

Popular Methods to Solve Linear Equation with two variables are substitution method, elimination method.

2. How to Solve Linear Equations with two variables?

You can solve linear equations with two variables taking the help of our Linear Equation with two variables Calculator.

3. How many solutions are there for linear equations with two variables?

For linear equations with two variables, there are infinitely many solutions.

4. What is the general representation for Linear Equations with two variables?

General Representation to denote Linear Equation in two variables is ax+by+c =0 where a, b is not equal to 0.

Learn how to use the Algebra Calculator to solve systems of equations.

Example Problem

Solve the following system of equations:
x+y=7, x+2y=11

How to Solve the System of Equations in Algebra Calculator

First go to the Algebra Calculator main page.

Type the following:

1. The first equation x+y=7
2. Then a comma ,
3. Then the second equation x+2y=11

Try it now: x+y=7, x+2y=11

Clickable Demo

Try entering x+y=7, x+2y=11 into the text box.

After you enter the system of equations, Algebra Calculator will solve the system x+y=7, x+2y=11 to get x=3 and y=4.

More Examples

Here are more examples of how to solve systems of equations in Algebra Calculator. Feel free to try them now.

• Solve y=x+3, y=2x+1: y=x+3, y=2x+1
• Solve 2x+3y=5, x+y=4: 2x+3y=5, x+y=4

Need Help?

Please feel free to Ask MathPapa if you run into problems.

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• Algebra Calculator Tutorial

When an applied problem requires that more than one unknown quantity must be found, it is often helpful (or, in some cases, absolutely necessary) to write several equations in several variables, and then solve this resulting system of equations. At the college algebra level, we usually restrict the number of unknowns to two or three. After studying this chapter, it will become clear how the methods of solving systems can be extended to a larger number of unknowns. Graphing calculators and computers are able to solve systems of equations, eliminating the need for time-consuming computations. The methods of this chapter (especially those in can help the student appreciate the capabilities of today's electronic marvels.

Many applications of mathematics require the simultaneous solution of a large number of equations or inequalities having many variables. A group of equations that place restrictions on the same variables is called a system of equations. The solution set of a system of equations is the intersection of the solution sets of the individual equations. It is customary to write a system by listing its equations. For example, the system of equations  2x + y = 4 and x - y = 6 is written as

In general, a first-degree equation in n unknowns is any equation of the form

where a_1, a_2, . . . , a_n, and k are constants and x_1, x_2, . . . , x_n are variables. Such equations are also called linear equations. Generally, only systems of linear equations with two or three variables will be discussed in this book, although the methods used can be extended to systems with more variables.

The solution set of a linear equation in two variables is an infinite set of ordered pairs. Since the graph of such an equation is a straight line, there are three possibilities for the solution set of a system of two linear equations in two variables. An example of each possibility is shown in the figure below.

Possible graphs of a linear system with two equations and two variables

1. The graphs of the two equations intersect in a single point. The coordinates of this point give the solution of the system. This is the most common case. See Figure (a).
2. The graphs are distinct parallel lines. In this case, the system is said to be inconsistent. That is, there is no solution common to both equations. The solution set of the linear system is empty. See Figure b.
3. The graphs are the same line. In this case, the equations are said to be dependent, and any solution of one equation is also a solution of the other. Thus, there are infinitely many solutions. See Figure c.

Although the number of solutions of a linear system can often be seen from the graph of the equations of the system, it is usually difficult to determine an exact solution from the graph. A general algebraic method of finding the solution of a system of two linear equations, called the substitution method, is illustrated in the following example and used again later.

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