# Solving Equations with MATLAB's Symbolic Toolbox

## Introduction

MATLAB's Symbolic Math Toolbox allows you to solve algebraic equations symbolically, making it easy to find exact solutions to mathematical problems. In this guide, we'll introduce you to solving equations using the Symbolic Toolbox with sample code.

## Creating Symbolic Variables

To work with symbolic equations, you need to create symbolic variables. Here's how you can define symbolic variables:

``% Example: Creating symbolic variablessyms x y z;    ``

## Solving Algebraic Equations

MATLAB's Symbolic Toolbox can be used to solve algebraic equations symbolically. Let's solve a simple equation:

``% Example: Solving a simple equationequation = x^2 - 4 == 0;solutions = solve(equation, x);    ``

## Solving Systems of Equations

You can also solve systems of equations with multiple variables:

``% Example: Solving a system of equationseq1 = 2*x + y == 5;eq2 = 3*x - y == 1;[sol_x, sol_y] = solve([eq1, eq2], [x, y]);    ``

## Symbolic Calculations

The Symbolic Toolbox allows you to perform symbolic calculations, such as differentiation and integration:

``% Example: Differentiate and integrate symbolicallyderivative = diff(x^3, x);  % Differentiate x^3 with respect to xintegral_result = int(2*x, x);  % Integrate 2x with respect to x    ``

## Conclusion

This guide has introduced you to solving equations with MATLAB's Symbolic Toolbox. Symbolic math capabilities are essential for various mathematical and engineering tasks, making MATLAB a versatile tool for performing symbolic calculations. As you gain experience, you can explore more advanced symbolic math features and techniques.

Enjoy finding exact solutions to equations with MATLAB's Symbolic Toolbox!