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Solve the following system of linear equations : 2(ax – by) + (a + 4b) = 0, 2(bx + ay) + (b – 4a) = 0 - Mathematics

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Sum

Solve the following system of linear equations :

2(ax – by) + (a + 4b) = 0

2(bx + ay) + (b – 4a) = 0

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Solution

2ax – 2by + a + 4b = 0 …. (1)

2bx + 2ay + b – 4a = 0 …. (2)

Multiplyng (1) by b and (2) by a and subtracting, we get

`2(b^2 + a^2 ) y = 4 (a^2 + b^2 ) ⇒ y = 2`

Multiplying (1) by a and (2) by b and adding, we get

`2(a^2 + b^2 ) x + a^2 + b^2 = 0`

`2(a^2 + b^2 ) x = – (a^2 + b^2 ) ⇒ x = – 1/2`

Hence x = –1/2, and y = 2

Concept: Algebraic Methods of Solving a Pair of Linear Equations - Elimination Method
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