What is a system of equations?
A system of equations is a set of equations (Usually two) that are solved together.
The solution is the point(s) where the equations intersect. However, there are three types of solutions. There could be:
There are also three ways to solve a system of equations. They are:
- Graphing the Equations
- Substitution
- Elimination
Both the Substitution and Elimination methods use algebraic manipulation to get rid of one variable, allowing you to solve for the remaining variable.
Tip: Different methods can be easier or harder to use based on the equation. By familiarizing yourself with the methods listed below, you can save time by choosing the best method.
Method 1 – Graphing the Equations
This method of solving systems of equations works by graphing the equations, and finding where they intersect. This method works best for easy to graph equations, or when you have access to a graphing calculator, or graphing software.
Example:
To double-check your answer, plug-in x and y into the corresponding spots in each of your equations. If you receive true statements from both of the equations your answer is correct. Otherwise, double-check your graph.
Related: The Maxopoly Recommended Graphing Calculator
Method 2 – Solving Through
Substitution
This method of solving systems of equations works by solving one equation for a variable, and substituting it into the second equation. This method works best for equations already solved for a variable, or when it can easily be solved for a variable.
Example:
To double-check your answer, plug-in x and y into the corresponding spots in each of your equations. If you receive true statements from both of the equations your answer is correct. Otherwise, double-check your substitution.
Method 3 – Solving Through
Elimination
Elimination is a method that subtracts or adds one whole equation to the other, which works to remove a variable. Then you can solve for the remaining variable, and get your solution. This method is useful when there is a equal absolute value amount of one variable in both equations.
Some sample equations could look like:
y = 2x + 3 and y = –2x + 4 (The x values would cancel out)
y = 3x – 3 and y = -3x + 5 (The x values would cancel out)
x + 4y = 4 and 2x – 4y = 5 (The y values would cancel out)
Example:
To double-check your answer, plug-in x and y into the corresponding spots in each of your equations. If you receive true statements from both of the equations your answer is correct. Otherwise, double-check your elimination.
Related: Maxopoly Recommended Free Graphing App
