A linear equation is an equation whose graph is a straight line. Two or more linear equations when worked together simultaneously then it is called systems of linear equations. In some equations there would be two variables, that is two unknowns that have to be solved. The solution of these equations would be the point of intersection of the two straight lines when they intersect.
When the linear equations that are worked together have two unknowns it is called systems of linear equations in two variables. Examples: 2x-3y=1 and x+2= - 3y. The solution of a system of equations in two variables is an ordered pair which satisfies both the equations, which means when the ordered pair is substituted in each of the equations then it is true.
The system of linear equations is said to be a consistent system if it has at least one solution that is at least one ordered pair that satisfies both the equations. It is said to be an inconsistent system if it has no solution. If all solutions of one equation are the solutions of the other equation then the equations are said to be dependent, which means they are the same line.
If they do not share all the solutions the system of equations are said to be independent to each other which means they have one point in common and not all.
The possible outcomes while working with linear equation in two variables are one solution, no solution or infinite solutions. If the lines intersect at one point, then that point of intersection (one ordered pair) becomes the solution of the equations.
If the lines are parallel then there would be no solutions. If the lines overlap on each other then there would be infinite number of solutions as they would be different equations for the same line.
There are different methods which can be used in solving an equation with two variables, which are:
In the graphing method, the graph of each of the linear equations is plotted and the point of intersection would be the solution. In Elimination method, one of the variables is eliminated using the opposite operation method and the solution is found using series of steps.
In substitution method, one variable is written in terms of the other which is later substituted in the second equation and then solved. Linear Equation Graph maker is a tool that helps in graphing the equations to get the solutions.