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# Systems of Linear and Quadratic Equations Calculator + Online Solver With Free Steps

The online **Systems of Linear and Quadratic Equations Calculator** helps you solve math problems, including linear and quadratic equations with up to 3 variables. This calculator gives you a complete solution for any system of equations.

**Linear and quadratic** equations are algebraic systems of equations. The goal of solving this system of equations is to simplify the complex equations having two or three variables to a single equation or find the values of variables.

## What Is the Systems of Linear and Quadratic Equations Calculator?

**Systems of Linear and Quadratic Equations Calculator is an online tool that gives the values of variables of the system of equations.**

This **system of equations** may include linear or quadratic equations. This calculator is a handy tool for determining the values of variables and solving linear and quadratic equations.

The system of equations is one of the most fundamental and applied concepts in the field of** Algebra**. Solving the system of equations is lengthy and becomes even more complex if there are more than two variables.

This concept has **deep practical applications** in our daily life. Linear equations are used to calculate the parameters for moving objects, link speed, distance time, etc. These equations can be used to solve money and percentage-related problems.

**Linear Equation**s also have applications in problems, including work, time, etc. Similarly, the quadratic equation system can help calculate areas and solve problems related to the profit or speed of objects.

## How To Use the Systems of Linear and Quadratic Equations Calculator?

You can use the **Systems of Linear and Quadratic Equations Calculato**r by entering the equations in the spaces provided for each equation. You have to enter at least two equations for the calculations. The solution of fewer than two equations does not exist.

The procedure to use the Systems of Linear and Quadratic Equations Calculator is very simple. You need to follow the simple steps mentioned below.

### Step 1

Enter the first equation in the first box labeled **Equation 1**. Similarly, enter the second equation in the text box labeled **Equation 2**. Depending on the situation, you can add a third equation also in the box labeled Equation 3.

### Step 2

Now, click on the **‘Submit’ **button to get the results.

### Result

Once you press the **submit **button, a new window pops up. This window shows the detailed result. It consists of** four sections**. The **first section **shows the input details for verification purposes.

**Section two **gives the real solution to equations. This also has two options. You can see the exact form or the approximate solution. The **third section **shows the normal solution to the problem concerning variables.

**The fourth **and the last section give the integer solution to the problem.

## How Do the Systems of Linear and Quadratic Equations Calculator Work?

**The Systems of Linear and Quadratic Equations Calculator** works by finding the values of variables involved in the system of equations by simultaneously solving them.

Before we move ahead, we should know some basics about the systems of linear and quadratic equations; then, we will also solve examples to clarify the concepts thoroughly. So below are some prerequisite concepts.

### What Is a Linear Equation?

A **linear Equation **is an algebraic equation in which the highest power of variables is one. Plotting a linear equation in a graph gives a **straight line**. That’s why it is known as a linear equation.

#### Standard Form of Linear Equations

**The standard form **of a linear equation in a single variable is given as:

**Ax + By = 0**

Here, A and B are real numbers, and x is a variable. The standard equation for two variables is given as:

**Ax + By = C**

**What Is a Quadratic Equation?**

**A quadratic equation** is an algebraic equation in which the highest power of variables is 2. A quadratic equation is plotted in a graph and gives a **parabola**. It is also known as a second-order equation.

As the higher power in the quadratic equation is 2, it is known as a quadratic equation because **quad means square**.

**Standard Form of Quadratic Equations**

The **standard form **of a quadratic equation is given as:

**ax^2 + bx + c = 0**

Here:

**a **is the coefficient of x^2

**b **is the coefficient of x

**c **is the constant

**What Is a System of Equations in Mathematics?**

A** system of equations** in mathematics is a set of equations that are dealt with simultaneously, or we deal with them all together. These equations share the variables. The equations involving two variables can be solved using substitution, elimination, and graphical methods.

The equations with more than two variables can be solved using **matrices**, **addition, ****subtraction, elimination**, etc.

## Solved Example

Now let’s solve a real-life example to understand the working of the Systems of Linear and Quadratic Equations Calculator. The example is described below:

### Example 1

A boy playing a cannon game shoots the ball with cannon. The ball flies through the air in the shape of a parabola. Let’s say the equation of a parabola is

**Y = 5 + 2x – 0.2x^2**. The upward slope of the land is 2x. Find the point where the ball lands.

### Solution

From the given data, we get two equations:

**y = 5 + 2x – 0.2x^2……….eq 1**

**y = 2x………………………eq 2**

These equations will be put in the provided boxes of the calculator.

The calculator will solve these equations simultaneously as:

Both sides are equal to y, so,

**5 + 2x – 0.2x^2 = 2x**

**2 + 2x – 0.2x^2 – 2x = 0**

**2 – 0.2x^2 = 0**

**0.2x^2 = 2**

**x^2 = 10**

**x = √10**

**x = ±3.1622**

The calculator takes the positive value.

So,

**x = 3.1622**

Now puts the value of x in eq 2:

**y = 2(3.1622)**

**y = 6.3244**

So the point where the ball lands is **(3.1622, 6.3244)**