Simultaneous Equations Calculator

Simultaneous Equations Calculator

Enter the equations into simultaneous equations calculator and get instant solution of system of equations.

Ask Your Question

Scan the QR code to upload a photo

For Detail Answer

Simultaneous Equations Calculator

This simultaneous equations solver is used to solve a wide range of systems of 2, 3, 4, 5 simultaneous equations. You can get solutions for linear and nonlinear equations including polynomial, rational, exponential, logarithmic, trigonometric, and hyperbolic equations. Our tool makes your calculations faster and shows the variables (x and y) quickly.

What are Simultaneous Equations?

“Simultaneous equations are a set of two or more algebraic equations with multiple variables solved at the same time.”

For Example: Consider the following two linear equations:

2x + 3y = 6
x - y = 2

In this case, x and y are the variables. Solving this system involves finding the values of x and y that make both equations true at the same time.

How to Use Simultaneous Equation Solver?

Enter equations into the simultaneous equation calculator
Click on “Calculate” to get an instant and accurate solution
Our simultaneous equations calculator gives you the answer as variables x and y of the simultaneous equations

What are the Methods For Solving Simultaneous Equations?

There are three ways to solve simultaneous equations. These including:

Substitution method
Elimination method
Augmented matrix method

Substitution Method:

In this method, we solve one equation for one variable and then put that expression into the other one. This simplifies the system to a single equation with one variable making it possible to find a solution.

Elimination Method:

This approach uses addition or subtraction of the equations to remove one of the variables.

Augmented Matrix Method:

This system involves representing the systems of equations as an augmented matrix. This consists of coefficients and constants. Generally, this method is used to solve large systems of equations.

Example:

Let's say you have two numbers, x and y.

Equation 1: x + y = 10
Equation 2: x - y = 2

Add the two equations

(x + y) + (x - y) = 10 + 2

2x = 12

x = 12 / 2

x = 6

Substitute x into equation # 1:

6 + y = 10

Solve for y:

y = 10 - 6

y = 4

x = 6
y = 4

FAQs:

What are Simultaneous Equations used for?

Simultaneous equations are used in situations involving multiple unknown quantities, given at least two or more informative relationships between them.

What are the types of simultaneous equations?

There are two types of simultaneous equations including:

Simultaneous linear equations
Simultaneous non-linear equations

What is the difference between linear and nonlinear simultaneous equations?

Linear Equation: An equation with the maximum degree of one is called a linear simultaneous equation.
Nonlinear Equation: An equation with a degree of maximum 2 or more than 2 is called a nonlinear equation.