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Systems of Equations: Graphical Method

In these lessons, we will learn how to solve systems of equations or simultaneous equations by graphing.

At the end of these lessons, we have a systems of equations calculator that can solve systems of equations graphically and algebraically. Use it to check your answers.

Related Topics:
Solve Systems of Equations by Substitution

Solve Systems of Equations by Addition Method (Opposite-Coefficients Method)

More Algebra Lessons

Solve System of Equations by Graphing

To solve systems of equations or simultaneous equations by the graphical method, we draw the graph for each of the equation and look for a point of intersection between the two graphs. The coordinates of the point of intersection would be the solution to the system of equations. If the two graphs do not intersect - which means that they are parallel - then there is no solution.


Using the graphical method, find the solution of the systems of equations

y + x = 3
y = 4x - 2


Draw the two lines graphically and determine the point of intersection from the graph.
From the graph, the point of intersection is (1, 2)

How to Solve Systems of Equations Graphically?
A system of equations is a set of two or more equations that are to be solved simultaneously.
What can happen when two lines are graphed on the same coordinate plane?
1. The graphs intersect at one point. The system is consistent and has one solution.
2. The graphs are parallel. The system is inconsistent because there is no solution.
3. Equations have the same graph. The system is consistent and has an infinite number of solutions. This is called a dependent system.
Some examples on solving systems of equations graphically.

Solving a Linear System of Equations by Graphing.
Have a look at the following video for another example on how to solve systems of equations using the graphical method:


Systems of Equations Calculator

This math tool will determine the intersection point of two lines or curves. Enter in the two equations and submit. The graphs of the two equations will be shown. Select step-by-step solution if you want to see the equations solved algebraically.

You can use the Mathway widget below to practice Algebra or other math topics. Try the given examples, or type in your own problem. Then click "Answer" to check your answer.

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