# Solving System of Linear Equations using Inverse Matrix (4 Variables)

**Solving System of Linear Equations using Inverse Matrix (4 Variables)**: Take advantage of our handy Solving System of Linear Equations using Inverse Matrix (4 Variables) Calculator to find the addition of any 4 fractional equations easily. You just have to input the fractions as inputs and tap on the calculate button to get the result in no time.

### What is meant by Linear Equation?

In mathematics, a linear equation is defined as an expression where each term in the variable has an exponent of one. If it is represented in a graph then it results in a straight line. The straight-line equation y=mx+c is an example of a linear equation.

Generally, the form of linear equation is Ax+B=C, where A, B, C are constants and x is variable. Moreover, the linear equations can be written in three distinct ways, they are

- Linear equation in one variable
- Linear equation in two variables
- Linear equation in three variables

Solving the linear equations calculator find the solution of the variable for a given equation within seconds.

### Examples of Solving System of Linear Equations using Inverse Matrix (4 Variables)

**Question 1: Solve the problem of finding a system of Linear Equations using Inverse Matrix (4 Variables)**

** 78 ๐ฅ _{1 } + 88 ๐ฅ_{2 } + 56 ๐ฅ_{3 } + 8 ๐ฅ_{4 }= 89**

** 2 ๐ฅ _{1 } + 3 ๐ฅ_{2 } + 0 ๐ฅ_{3 } + -1 ๐ฅ_{4 }= -1**

**-3 ๐ฅ _{1 } + 4 ๐ฅ_{2 } + 1 ๐ฅ_{3 } + 2 ๐ฅ_{4 }= 10**

** 1 ๐ฅ _{1 } + 2 ๐ฅ_{2 } + -1 ๐ฅ_{3 } + 1 ๐ฅ_{4 }= 1**

**Solution :**

#### As A * A^{-1} = I

#### where I is the identity matrix of 4 x 4

#### Step-1 ----> R2 -> R2 - R1*0.0256

Step-2 ----> R3 -> R3 - R1*-0.0385

Step-3 ----> R4 -> R4 - R1*0.0128

Step-4 ----> R3 -> R3 - R2*9.9309

Step-5 ----> R4 -> R4 - R2*1.1724

Step-6 ----> R4 -> R4 - R3*-0.002

Step-7 ----> R3 -> R3 - R4*6.1045

Step-8 ----> R2 -> R2 - R4*-0.5153

X = A^{-1}. B

**Answers**

**โ x**_{1} = -0.53

_{1}= -0.53

**โ x**_{2} = 0.9

_{2}= 0.9

**โ x**_{3} = 1.29

_{3}= 1.29

**โ x**_{4} = 1.83

_{4}= 1.83

### FAQs on Solving System of Linear Equations using Inverse Matrix (4 Variables)

**1. How do non-linear equations form?**

Generally, a non-linear equation is given by ax²+by² = c, where a,b,c are constant values and x, y are variables.

**2. How can I Solve a Solving System of Linear Equations using Inverse Matrix (4 Variables) in a fraction of a second?**

You can easily & quickly solve a system of Linear Equations using an Inverse Matrix (4 Variables) by using Linearequationscalculator.com offers a free online & handy Linear Equations in Two Variables Calculator.