![]() A consistent system of equations has at least one solution. In addition to considering the number of equations and variables, we can categorize systems of linear equations by the number of solutions. For example, consider the following system of linear equations in two variables.Ģ ( 4 ) + ( 7 ) = 15 True 3 ( 4 ) − ( 7 ) = 5 True \begin 2 ( 4 ) + ( 7 ) = 15 True 3 ( 4 ) − ( 7 ) = 5 True In this section, we will look at systems of linear equations in two variables, which consist of two equations that contain two different variables. Even so, this does not guarantee a unique solution. In order for a linear system to have a unique solution, there must be at least as many equations as there are variables. ![]() Some linear systems may not have a solution and others may have an infinite number of solutions. To find the unique solution to a system of linear equations, we must find a numerical value for each variable in the system that will satisfy all equations in the system at the same time. Solve a system of linear equations by graphingĪ system of linear equations consists of two or more linear equations made up of two or more variables such that all equations in the system are considered simultaneously. ![]()
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