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

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### What is meant by Solving System of Linear Equations using Inverse Matrix (2 Variables)?

A linear equation having only two variables with a degree of two is called a linear equation with two variables. The **Solving System of Linear Equations using Inverse Matrix (2 Variables)** is the value of the variable.

If we consider the example of Solving a System of Linear Equations using an Inverse Matrix (2 Variables). If we draw the equation graphically then it appears as a straight line in the vertical or horizontal direction.

### Examples On Linear Equation In two variables

**Example:**

Solve x + y = 4 and x + 2y = 6

**Solution:**

Given linear equations are

x + y = 4 ……….(1)

x + 2y = 6 ……...(2)

From (1), x = 4 - y ……..(3)

Substitute (3) in (2),

x + 2y = 6

4 - y + 2y = 6

4 + y = 6

Subtract 4 on both sides of the equation

4 + y - 4 = 6 - 4

Y = 2 ………(4)

Substitute (4) in (1)

x + y = 4

x + 2 = 4

Subtract 2 on both sides of the equation

x + 2 - 2 = 4 - 2

X = 2

Hence, x = 2 and y = 2 are the variable values for the given linear equations.

### FAQs on Solving System of Linear Equations using Inverse Matrix (2 Variables)

**1. How many solutions have Linear Equations with Two Variables?**

Let’s assume that you have a1x + b1y + c1= 0 and a2x + b2y + c2 = 0 the solutions of a linear equation with two variables are:

One and unique if a1a2 ≠ b1b2

None if a1a2 ≠ b1b2 ≠ c1c2

Infinitely many if a1a2 = b1b2 = c1c2

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

You can easily & quickly solve a system of Linear Equations using an Inverse Matrix (2 Variables) by using Linearequationscalculator.com offers a free online & handy Linear Equations in Two Variables Calculator.