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Substitution Calculator

Substitution Calculator


Calculation For:

\begin{cases} \text{$a_1x + b_1y = k_1$}\\ \text{$a_2x + b_2y = k_2$}\\ \end{cases}

\begin{cases} \text{$a_1x + b_1y + c_1z = k_1$}\\ \text{$a_2x + b_2y + c_2z = k_2$}\\ \text{$a_3x + b_3y + c_3z = k_3$}\\ \end{cases}




















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The substitution calculator is used to solve the substitution of the linear equations. It can be easy to find the substitution of the two or three linear equations at a time. This can be great for increasing the understanding of the substitution process when we are using the substitution method.

So let’s move on and learn more about the concept!

The definition of the substitution method:

“In the substitution method we calculate the value of one variable from one equation and substitute it into another equation.”
We actually transform both the linear equation system into one equation and have one variable. We are easily able to solve each system by substitution and convert both the equations into one. The substitution  calculator makes the task simple and elaborative.
It actually displays all the steps of the substitution in the output result. This is best for the students who want to learn the substitution method.

Method of solving the algebraic equation:

We can solve the algebraic equation by the following major methods:
The algebraic method

  • The algebraic method 
  • Graphical method

The algebraic method of the solving the linear equation is subdivided into the three major methods:

  • The substitution method
  • The elimination method
  • The cross-multiplication method

The substitution method is the most common algebraic method of finding the solution of the algebraic equations along with the elimination method. It is easy to understand and solve the algebraic equation by these methods. We can utilize the substitution calculator to find the solution of the equation.

The step involved in the substitution process:

There are 3 basic steps involved in the substitution process:

  1. We first solve one equation and get the value of one variable. 
  2. In the second step we plug in the values in the second equation.
  3. In the third step we actually again substitute the values into the original equation to find the final value of our variables.

The graphical method:

The graphical method is commonly known as the geometric method. In this method we actually draw a straight line and find the solution of the simultaneous equation. The result is the corresponding substitution points of both the equation:

It is best to use the system of equations calculator, when we are solving a system of equations linear in nature then.

How can we understand the system of linear equations?

It may be a little odd for you that we are using the word the system of linear equations. The equation involved in finding the values of the variables “x” and “y”. These equations are solved simultaneously to find the values of variables. Below we are presenting the generic form of the system of the line equation. We solve the substitution system of equations by taking the value from one system and putting the values in the other equation. The substitution calculator readily solves the linear equation substitution.
ax + by = k1
cx + dy = k2
The “x” and “y” are the variables in both the linear equations.
The “a”,”b”, “c” and “d” are the coefficients of the linear equation
In both equation the “k1” and “k2” are the constant

Practical examples of the substitution:

It is essential to elaborate the substitution process by practical examples. The linear system of equations calculator is going to solve the linear equation by the substitution methods:

Example 1:
Consider the system of linear equations
2x + 4y = 4———-(Eq1)
x + y = 3———-(Eq2)
We first find the values of “x” from the (Eq2)
x = 3 – y
In the substitution method calculator we insert the values of the “x” in the (Eq1)

2 ⋅ (3 – 1y) + 4y = 4
Solving by substitution, we find the value of variables “y”
2y = -2
The value of “y” in (Eq1)
y = -1
y = -1 in the
2x + 4 ⋅ (-1) = 4
The value of “x”
x = 4
The final values of the “x” and “y”
x = 4 , y = -1

Example 2:
Now Consider another system of linear equations
2x + 2y = 4———-(Eq1)
3x + 6y = 6———-(Eq2)
We are using the (Eq1) to the values of “x”
2x = 4 – 2y
Next, divide both sides by 2:
x = 2 – y
Now Substitute x into the (Eq2):
3 ⋅ (2 – 1y) + 6y = 6
The value of the variable “y” is
y = 0
Substituting y = 0 into the (Eq1) we get:
2x + 2 ⋅ 0 = 4
We get the values of the variable “x”
x = 2
Final Solution:
x = 2 , y = 0

The working of the systems of equations calculator:

The substitution calculator is simple to use and efficient in solving the substitution of linear equations. Let’s have a look at its working!
Enter the coefficient in the designated field
Enter the constant values of both the equation as well
At last, hit the calculate button
The substitution calculator is simple to use and displays the results swiftly.
Displays the values of variables “x” and “y”
All steps of substitution are shown in detail


What is difference between the substitution and elimination method:

In the substitution calculator we take the value of one variable from one equation to the other. In the elimination method we cut down the “x”and “y” by making their coefficients the same. We can use substitution and elimination calculator to solve substitution.

Why do we need the substitution of algebraic linear equations ?

We are required to implement the substitution process to find the values of the variables “x” and “y” in a system of linear equations. The substitution calculator with steps elaborate all the steps of the substitution process.

What is the checking process of the substitution process?

When we get the output values of the variables “x”and “y”, then we insert them in any linear equation.If the left and right sides of the equation are equal then we know we have found correct values of “x” and “y”.

What do simultaneous linear equations mean in algebra?

We are finding the points which are common in both the linear equations, and the values of the “x” and “y” are points of interaction of the two equations.We are calling them simultaneous linear equations as these are making a system of linear equations together.

Can a substitution method be used to solve the system of equations of three equations?

Yes,We can solve three linear equations by the substitution method. The
systems of equations calculator is efficient to find the substitution of the three linear equations.


The substitution method is the most common method to solve a system of simultaneous linear equations. We do require the values of variables to find the common point of the linear equation. The systems of equations calculator is a simple and swift way to find the solution of the linear equations.


From the source of Wikipedia: Substitution (logic),Propositional logic

From the source of calcworkshop :What is the SubstitutionSubstitution Method