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Solve the following equations by inversion method: x + y = 4, 2x - y = 5 - Mathematics and Statistics

Sum

Solve the following equations by inversion method:

x + y = 4, 2x - y = 5

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Solution

x + y = 4,  2x - y = 5

The given equations can be written in the matrix form as:

`[(1,1),(2,-1)] [("x"),("y")] = [(4),(5)]`

This is of the form AX = B ⇒ X ⇒ A-1B

A = `[(1,1),(2,-1)]`

|A| = - 1 - 2 = - 3 ≠ 0

Adj A = `[(-1,-1),(-2,1)]`

` = 1/-3[(-1,-1),(-2,1)] = [(1,1),(2,-1)]`

X = A-1B = `[("x"),("y")] = [(1,1),(2,-1)] [(4),(5)]`

`= [(4,5),(8,-5)] = [(9),(3)]`

`= [(3),(1)]`

By equality of matrices,

x = 3, y = 1.

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