System of Equations Calculator: The best tool to solve systems of equations
System of Equations Calculator
We present you the best System of Equations Calculator with steps , with which you can solve systems of linear equations, system of quadratic equations, linear quadratic systems and system of nonlinear equations in general.
This calculator is ideal for learning to solve systems of equations by substitution and elimination methods, since it presents solutions explained step by step. So if you are studying algebra, this system of equations calculator will be of great help to you.
This calculator is ideal for learning to solve systems of equations by substitution and elimination methods, since it presents solutions explained step by step. So if you are studying algebra, this system of equations calculator will be of great help to you.
And if you are a math teacher, this tool will help you create new teaching material to use in the classroom.
In the next section you will find the instructions to use the system of equations solver.
Instructions for using the System of Equations Solver
To solve systems of equations with this calculator follow these steps:
- Enter the equations one by one using the input field and the “+ Add” button. The entered equations will be located below the input field, you can edit them by pressing the button with the pencil icon or delete them by pressing the red “x” button.
- Press the “Solve” button to obtain the solution to the system of equations. A box with the detailed step-by-step solution will automatically be displayed. From this box you can choose the method used to solve the system of equations.
Here is a video tutorial showing in more detail how to use the system of equations calculator.
What is a system of equations?
A system of equations is a set of two or more algebraic equalities with several unknowns, these equalities are related to each other since the value of the unknowns satisfy all the equations. Example:
| 5x-3y+4z=-1 |
| -3x-6y=14z |
| 4x+8z=12 |
Types of systems of equations
Systems of equations can be classified according to different criteria.
If we take into account the degree of the equations, the systems of equations can be classified into:
- Linear system: if all the equations are linear.
- Nonlinear system: if not all equations are linear.
On the other hand, systems of equations can also be classified according to the number of equations or unknowns:
- Systems of two equations or Systems of two unknowns.
- Systems of three equations or Systems of three unknowns.
- etc. . . . .
Depending on the type of solutions, a system of equations can be classified as:
- Specified supported system. It is a system that has only one solution.
- Undetermined compatible system. An indeterminate compatible system has infinitely many solutions.
- Incompatible system. An incompatible system has no solution.
How to solve system of equations
The most used algebraic methods to solve systems of equations are the following:
• Substitution method
• Elimination method
The System of equations calculator uses the substitution and elimination methods.
It is important to keep in mind that the solution of a system of equations must be the same regardless of the method used to solve it. Each of the previously presented methods will be explained below and to make the explanation easier to understand, we will show how to solve the following system of equations using the three methods:
| 5x-32y=-1 |
| -3x-6y=14 |
Method of Substitution
It consists of isolating an unknown variable in one of the equations and substituting it in the other. Now we present how to solve by substitution the system shown above:
Elimination Method
In this method, the two equations are prepared so that one of the unknown variables has the same coefficient in both but with different signs. Adding the equations we get an equation with a single unknown variable.
