SOLVING LINEAR EQUATIONS IN 2 VARAIBLES USING INVERSION METHOD

Formula for inversion method :

X = A⁻¹ B

Example 1 :

Solve the following linear equation by inversion method

x + y = 3, 2x + 3y = 8

Solution :

First we have to write the given equation in the form

AX = B

Here X represents the unknown variables. A represent coefficient of the variables and B represents constants.

1	1
2	3

To solve this we have to apply the formula

X = A⁻¹ B

Since A is a non singular matrix. A⁻¹ exists.

x = 9 - 8

x = 1

y = -6 + 8

y = 2

Example 2 :

Solve the following linear equation by inversion method

2x - y = 7, 3x - 2y = 11

Solution :

To solve this we have to apply the formula X = A⁻¹ B

x = 14 - 11

x = 3

y = 21 - 22

y = -1

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