# 5.1 Solving Systems of Equations by Graphing and Substitution

A system of linear equations is two or more equations considered together. The solution of a system of linear equations is an ordered pair that is a solution to each equation in the system. The solution of a system of linear equations can be found by graphing the linear equations and finding the point of intersection. If they intersect at one point, the system is considered independent. If they do not intersect, they are considered inconsistent. If they intersect at every point, they are considered
dependent.

## Objective A – To solve a system of linear equations by graphing

If you need more practice solving systems by graphing, here is a worksheet with extra problems.

## Objective B – To solve a system of linear equations by the substitution method

At times, graphing does not produce an exact answer. The substitution method is one method used to find the exact solution to a system of linear equations.
Rewrite one equation in terms of either x or y. Substitute that value into the other equation. Solve for the remaining variable. Plug that result back in to one of the equations to get the other variable. The ordered pair (x,y) is the solution to the system of linear equations.

Here is a worksheet of systems of equations you can do using the substitution method.