- Home
- Math calculators

## Substitution calculator

Welcome to our Substitution Method Calculator! This tool is designed to help you solve systems of equations with ease.

Whether you’re a student, teacher, or just looking for a quick and reliable way to solve systems of equations, our Solve by Substitution Calculator is here to help. Give it a try now and see the magic happen!

To use this Substitution calculator to solve systems of equations, follow these steps:

- Enter each equation individually into the input field and click the “+ Add” button. The entered equations will appear below the input field. You can edit them by clicking the pencil icon button or delete them by clicking the red “x” button.
- Press the “Solve” button to find the solution to the system of equations. The Sustitution calculator will provide a detailed step-by-step solution, so you can understand how the solution was obtained. From this box, you can select the method used to solve the system of equations.

Table of Contents

- 1 Substitution calculator
- 2 What is the substitution method?
- 3 How to solve system of equations by substitution

## What is the substitution method?

The substitution method is a method used to solve systems of equations, which are a set of two or more equations containing multiple variables. The goal of the substitution method is to find the values of the variables that make all the equations in the system true simultaneously.

In the substitution method, we solve one of the equations for one of the variables in terms of the other variables, and then substitute this expression into the other equation. This results in a single equation with one variable, which we can solve to find the value of that variable. Once we have found the value of one of the variables, we can substitute it back into one of the original equations to find the value of the other variable.

The substitution method is useful when one of the equations in the system is easier to solve for one of the variables, or when the equations are already written in a form that is easy to substitute one into the other. It is generally a straightforward method, but it can be time-consuming if the equations are complex or if there are many variables.

## How to solve system of equations by substitution

Here’s a step-by-step guide to solving systems of equations by substitution:

Choose one of the equations and solve it for one of the variables in terms of the other variables. For example, if the equation is “2x + 3y = 6” and we want to solve for x, we can rearrange the equation to get “x = (6 – 3y)/2”. This gives us an expression for x in terms of y.

Substitute this expression for the variable into the other equation in the system. For example, if the other equation is “3x + 4y = 8”, we can substitute the expression for x that we found above to get “3((6 – 3y)/2) + 4y = 8”. This results in a single equation with one variable (in this case, y).

Solve the resulting equation for the value of the variable. For example, if we solve the equation “3((6 – 3y)/2) + 4y = 8” for y, we might get “y = 2”.

Substitute the value of the variable back into one of the original equations to find the value of the other variable. In this case, we could substitute the value of y (2) back into the equation “2x + 3y = 6” to find that “x = 0”.

So, the solution to the system of equations is (x, y) = (0, 2).

Here’s an example to illustrate the process:

Example: Solve the system of equations by substitution:

3x – 2y = 7

2x + y = 3

- Step 1: Solve the second equation for y: y = 3 – 2x
- Step 2: Substitute this expression for y into the first equation: 3x – 2(3 – 2x) = 7
- Step 3: Solve this equation for x:

3x – 6 + 4x = 7

7x – 6 = 7

7x = 13

x = 13/7

- Step 4: Substitute the value of x (13/7) back into the second equation to find y:

2(13/7) + y = 3

26/7 + y = 3

y = 3 – 26/7

y = -5/7

So, the solution to the system of equations is (x, y) = (13/7, -5/7).

**❤**