Systems of Equations
What is a System of Equations?
A system of equations is a set of at least two equations that have one solution that satisfies each equation simultaneously.
A system of equations can be solved graphically or algebraically using substitution or elimination.
It can also be solved using matrices.
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Systems of Equations Videos
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Systems of Equations Explained
As we’ve mentioned, a system of equations is a set of at least two equations where there is one solution that satisfies all of the equations within said system.
Here is an example of this:
The graph shown below is the graph of
y = 2x – 3.
You can see that each point labeled on the graph is a solution that satisfies the equation. In fact, the equation has infinite solutions because the graph has infinite points.
Look at the graph of the equation y = -3x + 7. Similarly, the graph has infinite solutions due to its infinite points.
Now, graph the two lines on top of each other and you will see that it has only one solution that will satisfy both equations at the same time.
This is the solution to a system of equations. In this particular example, we have a linear system of equations.
Graphs generated by Desmos.com
Just a heads up, though; some systems can have more than one solution, depending on the degrees of the equations, as shown with this next graph.
Graphs generated by Desmos.com
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