Simultaneous Equations Calculator for 2,3,4,5 Unknowns: With Step by step Solution/Explanation

Want to calculate? Get Solutions Here:

To calculate with the Simultanous Eqtn Solver

Enter Pairs or equations above separated Either ',' OR a ';' eg. x^2-y^2=4,2x-y=9 OR x^2-y^2=4,2x-y=9 Click the button to Solve!

Graphical Solution of Equations:

An online system of equations calculator with step by step solution

Simultanous equation calculator is an online tool that helps you solves systems of equations, It shows all the workings step by step. This powerful web tool is essential for determining solution to a system of equations. It can solve both linear and non-linear systems of equations with 2,3,4 or 5 unknowns.

Simultanous equation calculator is an online tool that solves systems of equations step by step. It Shows all the workings, it is accurate and convinient to use.

A perfect simultanous equations solver that helps you solve simultatious equations online.
The simultanous equation calculator helps you find the value of unknown varriables of a system of linear, quadratic, or non-linear equations for 2, 3,4 or 5 unknowns.
Our online system of equations calculator helps you to solve for any unknown varriables x,z, n, m and y
The simultaneous equation calculator above will help you solve simultaneous linear equations with two, three unknowns

A system of 3 linear equations with 3 unknowns x,y,z is a classic example. This solve linear equation solver 3 unknowns helps you solve such systems systematically

Linear equation represents relations between two or more variables. In nature, linear occur most often. Nevertheless, not all occurrences in nature are linear and therefore it is not easy to model natural events using linear relationships.

A linear equation, of the form ax+by=c will have an infinite number of solutions or points that satisfy the equation. To get unique values for the unknowns, you need an additional equation(s), thus the genesis of linear simultaneous equations.
In particular you need n to solve for n unknowns

An online Systems of linear Equations Calculator for solving simultanous equations step by step. Our system of equation solver shows you all the working, with a step by step solution. Our online algebra calculator for solving simultaneous equations is fast, accurate and reliable.

Before we learn how the linear simultaneous equations solver works, it would be best if we explored more on system of linear equations.

Finding the solution of a system of linear equations

A solution for a linear equation or system of linear equation is a set of co-ordinates in space that satisfy all the equations in a system. For a 2 dimensional case, the solution is a point in 2 dimensional co-ordinates that satisfy the given equations. In a 3 dimensional case, the solution is a point in 3d space that satisfies the given system of equations simultaneously. For higher degree cases, a similar analogy applies.

A system of linear equations may have:

  • Unique solution (solvable)
  • Infinitely may solution (inconsistent system)
  • Or no Solution at all

Solving systems of equations calculator Online

When a system of linear equations does have a unique solution?

Given any non-homogenous system of linear equation (n*n), the system will have a unique solution (non-trivial) if and only if the determinant of its coefficient matrix is non-zero. On the other hand the system will have infinitely many solutions if its determinant equal to zero.

For a system of equations with 2 unknowns, you need two equations to solve the system. Viewing the equations as straight lines in a 2d graph, a solution to the system is a point where the two lines intersect. A case of no solution means that the two lines never intersect; such lines are parallel to each other.


2x-3y=7, 4x-6y=9

Clearly, the two lines are parallel and therefore they will never intersect. For a 3 dimensional case, the given system of equations represents parallel planes.

On the other hand, the system of linear equations will have infinitely many solutions if the given equations represent line or plane in 2 and 3 dimensions respectively.

Solve simultaneous equations calculator

Our online calculator helps you find the solution to a system of equations instantly. The simultaneous equations solver also shows you all the steps and working. Here are some worked examples to show you a step by step solution for simultaneous equations

Solve simultaneous equations calculator

With the solving simultaneous equations calculator, you can do more calculations within a shorter duration. The simultaneous equations generator shows you the working too, therefore it is perfect for learning how to solve linear equations online.

How to solve a system of linear Equation

For a two dimensional case, we have 2 equations with 2 unknowns. There are 2 classical methods of solving such equations namely: Substitution and elimination Methods.

Substitution Method Calculator

This method involves first solving for one of the variables with one equation and then substituting the results in the second equation. Our algebra calculator has a substitution method option that lets you workout solution for simultaneous equation using the substitution method.

Substitution method calculator Examples

Substitution method calculator

Elimination method calculator with Workings

With our online algebra calculator, you can find solution to a system of linear equations using the elimination method.

The simultaneous equation solver is accurate, efficient and free. Elimination is one of the classical methods of solving a system of linear equations. In a two dimensional case, you first begin by selecting a particular variable that you want to eliminate.

 Let’s assume that our system is in x, y coordinates. For practicality, let’s start by eliminating x. First, you find a pair of factors such that multiplying them with the coefficients of x, in either equation makes the two equations to have a similar coefficient for x.

 Multiplying an equation by a scalar coefficient does not alter the equation. Once you have done the multiplication, subtract equation 2 from equation 1. By doing so, you will end up with an equation with only one unknown.

It is easy to solve an equation with one unknown. Once you have found the value, of x, substitute it back into any of the original equation to find the value of y.

Here are some worked examples to show solution by elimination method

elimination method calculator

Quadratic Simultaneous equations calculator with Working step by step

This calculator also helps you find solutions for a combination of quadratic and linear equations. Solution for such a system represents points of intersections between the curves (for a 2 dimensional case). Othersiwe, the solution may have a complex meaning when dealing with systems of higher order.Common examples include simultaneous equations with squares eg y^2+x^2=2;x+y=1

For a step by step solution for of any system of equations, nothing makes your life easier than using our online algebra calculator. Provided, that the vaiables can be separated/ factored, then it is posible to solve any system of equations using the substitution method. The simultaneous equations calculator is fast, efficient and reliable. It is an awesome simultaneous equations calculator with working.

How to use the simultaneous equations calculator online

First learn about supported problems here. Currently, the solver can deal with linear equations of 2, 3, 4, 5, 6 or 7 unknowns, mix of quadratic and linear equations, as well as non-linear problems. We are currently working to extend the scope of the calculator so that it can handle higher order systems of equations.

  1. Enter your equations separated by “;”or ‘,’. Once you have input your equations, hit the calculate button to get an instant solution.
  2. Scroll down to view the workings.
  3. You can latter print the solution using the “print solution Option”

Like our linear simultaneous equations solver? Or you have some new features that you would like to see included in the calculator? Send us a message and we shall be happy to implement them. You can send us a direct message through our email.

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Here is a Worked example to illustrate how the simultanous calculator Works:

Worked Algebra example

Learn how to solve simultanous equations algebraically with Examples

Perhaps it is best if you learnt math through examples. Checkout our algebra examples, each with a step by step solution. The Examples will also guide you on how to use this equation calculator to solve your algebra problems.

Go to Solved Algebra examples with Steps

Acceptable Math symbols and their usage
If you choose to write your mathematical statements, here is a list of acceptable math symbols and operators.

  • + Used for Addition
  • -Used for Subtraction
  • *multiplication operator symbol
  • /Division operator
  • ^Used for exponent or to Raise to Power
  • sqrtSquare root operator
Pi : Represents the mathematical Constant pi or \pi

What’s more or what are the limitations of the online algebra calculator

We love to hear your feedback. If you encounter any problems while using this calculator, please let us know: Want to see more features? Send us your recommendations and app ideas. We are always working hard to make algebra easy and fun.

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