# Solving System of Linear Equations using Augmented Matrix (2 Variables)

Free Online **Solving System of Linear Equations using Augmented Matrix (2 Variables) Calculator** will display the proper answer according to the given equation in a fraction of a second. Just you have to provide the valid expression in the input box and hit the calculate button to get the result for your given Augmented Matrix (2 Variables) in the output field.

### How to Solving System of Linear Equations using Augmented Matrix (2 Variables)?

The step-by-step process of solving the Solving System of Linear Equations using Augmented Matrix (2 Variables) is given here. Follow the steps carefully and learn manually to solve the equation:

- First, rearrange the equation by placing the constant terms on one side and the terms of the variable on another side by using arithmetic operations on both sides of the equation.
- Solve the calculations and eliminate the constants.
- Separate the variable on one side by adding on both sides of the equation.
- Simply calculate and find the value of the variable.

### Examples of Solving System of Linear Equations using Augmented Matrix (2 Variables)

**Question 1: Solve the problem of finding a system of Linear Equations using an Augmented Matrix (2 Variables).**

** 55 ๐ฅ _{1}**

_{ }

**+ 56 ๐ฅ**

_{2 }= 10** 45 ๐ฅ _{1}**

_{ }

**+ 8 ๐ฅ**

_{2 }= 12**Solution :**

Write the system of equations in matrix form.

Find the reduced row echelon form of the matrix.

**Answers**

Use the result matrix to declare the final solutions to the system of equations.

The last column of the final matrix denotes the values of x_{1}, and x_{2} respectively.

**โ x _{1} = 37 / 130**

**โ x _{2} = −21 / 208**

**Question 2: Solve the problem of finding a system of Linear Equations using an Augmented Matrix (2 Variables).**

** 15 ๐ฅ _{1}**

_{ }

**+ 63 ๐ฅ**

_{2 }= -88** 45 ๐ฅ _{1}**

_{ }

**+ 8 ๐ฅ**

_{2 }= 12**Solution :**

Write the system of equations in matrix form.

Find the reduced row echelon form of the matrix.

**Answers**

Use the result matrix to declare the final solutions to the system of equations.

The last column of the final matrix denotes the values of x_{1}, and x_{2} respectively.

**โ x _{1} = 292 / 543**

**โ x _{2} = −276 / 181**

### FAQs on Solving System of Linear Equations using Augmented Matrix (3 Variables)

**1. What is Linear Equation?**

A linear equation is an equation that gives a straight line when represented in a graph. It is an algebraic equation of the form y=mx+b.

**3. Which online tool is best for Solving a System of Linear Equations using an Augmented Matrix (3 Variables)?**

Linearequationscalculator.com is the best and most reliable website that provides a free online calculator for all topics of linear equations like Solving System of Linear Equations using Augmented Matrix (3 Variables), linear equations in one variable calculator, and more.