Created By : Abhinandan Kumar

Reviewed By : Rajashekhar Valipishetty

Last Updated : Oct 09, 2023

Enter the linear equation in the input field and tap the calculate button present in the online tool Solving System of Linear Equations using Cramers Rule(4 Variables) Calculator. Instantly, it calculates the equation and generates accurate results in no time.

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### How to Solve Solving System of Linear Equations using Cramers Rule(4 Variables)?

The step-by-step process of solving the Solving System of Linear Equations using the Cramers Rule(4 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 Cramers Rule(4 Variables)

Question 1: Solve the problem of finding a system of Linear Equations using the Cramers Rule(4 Variables)

78 ๐ฅ + 88 ๐ฅ +  56 ๐ฅ + 8 ๐ฅ= 89

5 ๐ฅ + 10 ๐ฅ +  5 ๐ฅ + 10 ๐ฅ= 56

65 ๐ฅ + 4 ๐ฅ +  1 ๐ฅ + 2 ๐ฅ= 10

1 ๐ฅ + 2 ๐ฅ +  -1 ๐ฅ + 1 ๐ฅ= 1

Solution :

Explaination - Δ

Step 1   R4 -> R4 - R3*0.0154

Step 2   R3 -> R3 - R2*13.0

Step 3   R2 -> R2 - R1*0.0641

Step 4   R4 -> R4 - R3*-0.0154

Step 5   R3 -> R3 - R2*-28.9057

Step 6   R4 -> R4 - R3*0.0861

In echelon form determinant of matrix is product of diagonals of matrix

Determinant of = (78)*(4.359)*(-23.2343)*(-13.5879)

Determinant = 107340.0

Determinant of = (89)*(-45.3708)*(-1.3686)*(0.2523)

Determinant = 1394.0

Determinant of = (78)*(50.2949)*(-43.8668)*(0.6334)

Determinant = -109012.0

Determinant of = (78)*(4.359)*(735.8099)*(1.0271)

Determinant = 256966.0

Determinant of = (78)*(4.359)*(-23.2343)*(-73.5384)

Determinant = 580936.0

•  x1 = Δ1/Δ = 1394.0/107340.0      x1 = 0.013
•  x2 = Δ2/Δ = -109012.0/107340.0    x2 = -1.0156
•  x3 = Δ3/Δ = 256966.0/107340.0    x3 = 2.3939
•  x4 = Δ4/Δ = 580936.0/107340.0   x4 = 5.4121

### FAQs on Solving System of Linear Equations using Cramers Rule(4 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.

2.  Which online tool is best for Solving a System of Linear Equations using Cramers Rule(4 Variables)?

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