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Solve the following system of equation in x and y.ax + by = 1 and bx + ay =2ab/a²b² |
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Answer» Answer: The given SYSTEM of EQUATIONS MAY be written as ax+by−1=0 bx+ay− a 2 +b 2
2ab
=0 By cross-multiplication, we have b×− a 2 +b 2
2ab
−a×−1 x
= a×− a 2 +b 2
2ab
−b×−1 −y
= a×a−b×b 1
⇒ a 2 +b 2
−2ab 2
+a x
= a 2 +b 2
−2a 2 b
+b −y
= a 2 =b 2
1
⇒ a 2 +b 2
−2ab 2 +a +ab 2
x
= a 2 +b 2
−2a 2 b+a 2 b+b 3
−y
= a 2 −b 2
1
⇒ a 2 +b 2
a 3 −ab 2
x
= a 2 +b 2
−a 2 b+b 3
−y
= a 2 −b 2
1
⇒ a 2 +b 2
a(a 2 −b 2 )
x
= a 2 +b 2
b(a 2 −b 2 )
−y
= a 2 −b 2
1
⇒x= a 2 +b 2
a(a 2 −b 2 )
× a 2 −b 2
1
and y= a 2 +b 2
b(a 2 −b 2 )
× a 2 −b 2
1
⇒x= a 2 +b 2
a
and y= a 2 +b 2
b
Hence, the solution of the given system of equations is x= a 2 +b 2
a
,y= a 2 +b 2 b. |
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