Question

Please solve this linear equation by cross multiplication method:
$ax + by = 1 \\ bx + ay = \frac{ {(a + b)}^{2} }{ {a}^{2} + {b}^{2}} - 1$
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Answer 1

Answer:

The given system of equations may be written as

ax+by−(a−b)=0

bx−ay−(a+b)=0

By cross-multiplication, we get

⇒ b×−(a+b)−(−a)×−(a−b) x

= a×−(a+b)−b×−(a−b)−y

= −a 2−b 21

⇒ −b(a+b−a(a−b)

x = −a(a+b)+b(a−b)−y = −(a 2+b 2) 1

⇒ b 2 −a 2x = −a 2 −b 2

−y = m−(a 2+b 2 )1

⇒ −(a 2+b 2 )

x= a 2+b 2y = −(a 2+b 2) 1

⇒x = −(a 2 +b 2 )−(a 2+b 2 ) = 1 and y= −( a 2 +b 2) ( a 2+b 2 ) = −1

Hence, the solution of the given system of equations is x=1, y = −1.

$thank \: you$