# Solving System of Linear Equations using Cramers Rule(2 Variables)

Enter the linear equation in the input field and tap the calculate button present in the online tool Solving System of Linear Equations using the Cramers Rule(2 Variables) Calculator. Instantly, it calculates the equation and generates accurate results in no time.

### How Many System of Linear Equations?

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 a linear equation is Ax+B=C, where A, B, and C are constants and x is a 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

### How to Solve Solving System of Linear Equations using Cramers Rule(2 Variables)?

The step-by-step process of solving the Solving System of Linear Equations using the Cramers Rule(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 Cramers Rule(2 Variables)

**Question 1: Solve the problem of finding a system of Linear Equations using the Cramers Rule(2 Variables) **

** 5 ๐ฅ _{1}**

_{ }

**+ 10 ๐ฅ**

_{2 }= 10** 5 ๐ฅ _{1}**

_{ }

**+ 8 ๐ฅ**

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

**1. Explanation - Δ**

** Step 1 R2 -> R2 - R1*1.0**

*Δ* =

** In the echelon form determinant of a matrix is a product of the diagonals of the matrix**

Determinant of = (5)*(-2.0)

** Determinant = -10.0**

**2. Explanation - Δ_{1}**

** Step 1 R2 -> R2 - R1*1.2**

*Δ* =

**In the echelon form determinant of a matrix is a product of the diagonals of the matrix**

Determinant of = (10)*(-4.0)

** Determinant = -40.0**

**3. Explaination - Δ_{2}**

** Step 1 R2 -> R2 - R1*1.0**

*Δ* =

**In the echelon form determinant of a matrix is a product of the diagonals of the matrix**

Determinant of = (5)*(2.0)

** Determinant = 10.03**

**Answers** -

โ x_{1} = Δ_{1}/Δ = -40.0/-10.0 ** x _{1} = 4.0**

โ x_{2} = Δ_{2}/Δ = 10.0/-10.0 ** x _{2} = -1.0**

### FAQs on Solving System of Linear Equations using Cramers Rule(2 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. How to express the standard form of a linear equation?**

The standard form of linear equations is Ax + By + C = 0 (A ≠ 0, B ≠ 0)where x and y are variables and A, B, and C are constants.

**3. Which online tool is best for Solving a System of Linear Equations using Cramers Rule(2 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 Cramers Rule(2 Variables) calculator, linear equations in one variable calculator, and more.