The system of equations in which two variables have a unique solution, no solutions, or infinitely many solutions is known as a linear equation in two variables. There might be as many as ‘n’ no of variables in the linear system of equations. When solving linear equations with n variables, it’s crucial to remember that there must be n equations to solve and find the values of variables. A straight line is the collection of answers found by solving these linear equations. The algebraic equations of the form y = mx + b, where m is the slope and b is the y-intercept, are known as linear equations in two variables. They’re called first-order equations.

## 2 variable linear equation

The linear equations in two variables have one, none, or infinitely many solutions and have the highest exponent order of 1. A two-variable linear equation has the conventional form ax+ by+ c= 0, where x and y are the two variables. It’s also possible to write the solutions in pairs. Two straight lines, which could be intersecting lines, parallel lines, or coincident lines, are included in the graphical representation of linear equations in two variables.

Suppose that we have an equation 3x + 4y = 6 then in this equation we have 2 variables that are x and y.

## Forms of linear equation in 2 variables

A 2 variable linear equation can have many distinct forms, including standard form of equations , intercept form, and point-slope form of equations. The same equation 2x+3y=9 can be written in a variety of ways, including 2x+3y-9=0 (standard form), y = (-2/3)x + 3 (slope-intercept form), and y – 5/3 = -2/3(x + (-2)). (point-slope form).

The term “system of equations” refers to a grouping of equations. We will learn how to solve two-variable linear equations using various strategies.

### Method to solve 2 variable linear equation:-

Rather than finding the solution to a single linear equation with two variables, we can find the solutions to two sets of linear equations, each with two variables. When there is more than one linear equation, the system of linear equations is defined. There are various ways to solve a two-variable system of linear equations. The following methods are given below in detail:

### Substitution method:-

To use the substitution method to solve a system of two linear equations in two variables, follow the procedures below:

Step 1: For each variable, solve one of the equations.

Step 2: Substitute this into the other equation to get a single-variable equation.

Step 3: Determine the variable.

Step 4: Substitute it for another variable’s value in any of the equations.

### Method of elimination:-

We’ll utilize the steps below to solve a system of linear equations in two variables using the elimination method:

Step 1: Put the equations in standard form, such as ax+by+c=0 or ax+by=c.

Step 2: Determine whether or whether adding or subtracting the equations cancels a variable.

Step 3: If not, multiply one or both equations by the x or y coefficients so that adding or subtracting them cancels out any of the variables.

Step 4: Solve the single variable equation that results.

Step 5: Substitute it for another variable’s value in any of the equations.

We are using generally two methods i.e. elimination method and substitution method to find the solution of 2 variable equations.

### Conclusion:-

If the equation is written in the form ax + by + c = 0, where a, b, and c are real integers and the coefficients of x and y which are a and b, are not equal to 0, it is said to be a linear equation in two variables. The solution to such an equation is a pair of values, one for x and one for y, that makes both sides of the equation equal.

A straight line is represented by a linear equation, as we all know. Plotting these graphs will assist us in solving equations with unknown variables.