How to Solve Linear Equations with Two Variables

System of linear equations contains number of equations with equal number of variables. For a linear system to have a definite solution, there must be at least as many equations as there are variables.
In addition to considering the number of equations and variables, we can categorize linear systems of equations by the number of solutions.
There are three types of linear equation systems in two variables and three types of solutions. Using different methods, students can easily determine the value of unknown. Students use graphic technology to explore the importance of solving a linear system, including solutions that match cut lines, parallel lines, and coincident lines.

How Many Solution has a Linear Equation in Two Variable?

Systems of equations have no solution, one unique solution or infinitely many solutions.
Equation systems are considered to be inconsistent with a solution as independent, with an infinite number of solutions as dependent or with no solution.

How do you Solve Linear Relationships?

Solving linear equations means to find the value of unknowns. There are different methods which help students to get the solution for given equations. Below we have listed some of the algebraic methods to solve the linear equations.

Use multiplication with a non-zero number so that one of the variables in one of the equations has the opposite coefficient of the same variable in the another equation, and then add or subtract the equations to remove the common variable.
Plug result to one the equations to find the value of the another variable,

To solve algebraic systems of equations containing two variables, such as x and y, first move the variables to different sides of the equation.
Substitute the result into the original equation to look for the other variable.

Enter your answer in one of the original equations so you can search for the other variable. Write the solution set as (x, y).

One of the methods of solving a system of linear equations in two variables is by graphing.
All linear equations are plotted as a straight lines on coordinate plane.
Graph of two equations, There will be 3 results: either lines are  intersecting, both the lines parallel to each other or coincides.
Result:
We get a false statement for inconsistent systems if parallel lines that never intersect or
we get a solution for the equations (consistent system).

Practice Problems

Practice below problems to check your knowledge.
Problem 1: x + y = 5 and 2x - y = 3
Problem 2: Solve pair of linear equations in two variables: 6x + 2y = -5 and 3x + y = 10
Problem 3: Solve using Elimination Method: 2x - y = 0 and 3x + y  = 5