No solution infinite solution one solution calculator

Q: What is the formula for no solution?

If (a1/a2) = (b1/b2) ≠ (c1/c2), then there will be no solution. This type of system of equations is called an inconsistent pair of linear equations. If we plot the graph, the lines will be parallel and system of equations have no solution.

This calculator solves Systems of Linear Equations using Gaussian Elimination Method, Inverse Matrix Method, or Cramer's rule. Also you can compute a number of solutions in a system of linear equations (analyse the compatibility) using Rouché–Capelli theorem.

Table of Contents Show

How to Use the System of Equations Calculator?
What is Meant by the System of Equations?
Solving system of linear equations
Our mission:
Lesson on Systems of Equations
Rules for Solving Systems of Equations
How to Solve a System
How the Calculator Works
Is 0 0 infinite or no solution?
What is an example of only one solution?
What is the formula for no solution?

Enter coefficients of your system into the input fields. Leave cells empty for variables, which do not participate in your equations. To input fractions use /: 1/3.

2x-2y+z=-3 x+3y-2z=1 3x-y-z=2

Leave extra cells empty to enter non-square matrices.
You can use decimal (finite and periodic) fractions: 1/3, 3.14, -1.3(56), or 1.2e-4; or arithmetic expressions: 2/3+3*(10-4), (1+x)/y^2, 2^0.5 (=2), 2^(1/3), 2^n, sin(phi), or cos(3.142rad).
Use ↵ Enter, Space, ←↑↓→, ⌫, and Delete to navigate between cells, Ctrl⌘ Cmd+C/Ctrl⌘ Cmd+V to copy/paste matrices.
Drag-and-drop matrices from the results, or even from/to a text editor.
To learn more about matrices use Wikipedia.

Enter System of Equations

x + y + z =
x + y + z =
x + y + z =

Solution :
x =
y =
z =

System of Equations Calculator is a free online tool that displays the variable value for the given set of equations. BYJU’S online system of equations calculator tool makes the calculation faster, and it displays the value of variables in a fraction of seconds.

How to Use the System of Equations Calculator?

The procedure to use the system of equations calculator is as follows:

Step 1: Enter the coefficients of the equations in the respective input field

Step 2: Now click the button “Solve these Equations” to get the result

Step 3: Finally, the solution for the given system of equations will be displayed in the output field

What is Meant by the System of Equations?

In Mathematics, the system of equations is defined as the collection or the set of equations. When the equations are solved, the solutions for the variables present in the equation can be obtained. We know that an algebraic equation consists of variables, constants, coefficients and exponents. While dealing with the system of linear equations, it can be observed that there are three different types of system of equations. They are:

A dependent system with infinitely many solutions
An independent system with exactly one solution
An inconsistent system with no solution

Solving system of linear equations

Write each equation on a new line or separate it by a semicolon. The online calculator solves a system of linear equations (with 1,2,...,n unknowns), quadratic equation with one unknown variable, cubic equation with one unknown variable, and finally, any other equation with one variable. Even if an exact solution does not exist, it calculates a numerical approximation of roots.

Examples:

x+y+z=100
3x-6y+2z=50
y-3z+x=(44-22)x+45

(x+4)(x-3)+34x+6x^2 = 256

Our mission:

Provide simple, fast, and reliable mathematical service for solving any equation(s).

More info:

Unknowns (variables) write as one character a-z, i.e., a, b, x, y, z. No matter whether you want to solve an equation with a single unknown, a system of two equations of two unknowns, the system of three equations and three unknowns, or a linear system with twenty unknowns. The number of equations and the number of unknowns should be equal, and the equation should be linear (and linear independent). Then you can be expected that the equations have one solution.
It is not necessary to write equations in the basic form. The calculator quickly performs equivalent operations on the given linear system.

Number of equations:

Equation 1:

Equation 2:

Lesson on Systems of Equations

Lesson Contents

Rules for Solving Systems of Equations

When solving a linear or nonlinear system of equations, we want to have a determined system where the number of equations is equal to the number of variables.

If there are fewer equations than variables, the system is underdetermined and may have zero or any number of solutions. If there are more equations than variables, the system is overdetermined and may have zero or any number of solutions.

A linear system of equations may have zero, one, or infinite solutions. A nonlinear system of equations may have zero or any number of solutions. There are zero solutions if the equations are parallel but never intersect. There are infinite solutions if the equations are identical and lay on top of each other over the entire domain.

How to Solve a System

There are many techniques available for solving a system of equations, however, they all leverage basic algebra, and any system of equations can be solved by isolating a variable, substituting it into another equation, isolating the next variable, and so forth.

Let’s solve a linear two-equation system using isolation and substitution. The system we will solve is:
Equation 1: 2x + y = 8
Equation 2: x – y = 4

Solution:
1.) Let’s isolate x in the second equation. Moving y to the right side of the equation results in x = y + 4.
2.) We may now substitute that value of x into the first equation. By doing so, we get 2(y + 4) + y = 8. Simplifying it results in 3y + 8 = 8.
3.) Solving that equation for y, we get y = 0.
4.) We may substitute y’s solution into either equation. Substituting it into the first equation, we get 2x + 0 = 8. Solving for x, we get x = 4.
5.) The solution to the system of equations is x = 4, y = 0.

How the Calculator Works

The Voovers System of Equations Solver is written in the programming language JavaScript (JS) and uses a JS native computer algebra system (CAS). Your device’s internet browser has a built-in JS engine, which allows the calculator to run locally and provide instant solutions.

When the calculate button is pressed, your equations are fed into a JS array that stores each equation in its own entry. Then, the array is fed to the CAS which performs the calculations that find the solution. For nonlinear systems, it returns the first solution that satisfies the equations.

After calculations are finished, the solution is converted to LaTeX (a math rendering language) and displayed in the answer area of the calculator. Sometimes there is no solution, infinite solutions, or an error during calculations. When these anomalies occur, an error message is displayed instead of an answer.

Is 0 0 infinite or no solution?

Since 0 = 0 for any value of x, the system of equations has infinite solutions.

What is an example of only one solution?

For example, 2x+3=8 is a linear equation having a single variable in it. Therefore, this equation has only one solution, which is x = 5/2.

What is the formula for no solution?

If (a₁/a₂) = (b₁/b₂) ≠ (c₁/c₂), then there will be no solution. This type of system of equations is called an inconsistent pair of linear equations. If we plot the graph, the lines will be parallel and system of equations have no solution.