solve the following pairs of lines equations by elimination method a) √2x-√3y=0 and √5x+√2y=0
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Given pair of linear equations is
√2 x – √3 y = 0 …(i)
And √5 x + √2 y = 0 …(ii)
On multiplying Eq. (i) by √2 and Eq. (ii) by √3 to make the coefficients of y equal, we get the equation as
2x – √6 y = 0 …(iii)
√15 x + √6 y = 0 …(iv)
On adding Eq. (iii) and (iv), we get
2x – √6 y + √15 x + √6 y = 0
⇒ 2x + √15 x = 0
⇒ x(2 + √15) = 0
⇒ x = 0
On putting x = 0 in Eq. (i), we get
√2 x – √3 y = 0
⇒ √2(0) – √3 y = 0
⇒ – √3 y = 0 ⇒ y = 0
Hence, x = 0 and y = 0 , which is the required solution.
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Answer:
x=0 and also y=0
√2x-√3y=0 -√2
√5x+√2y=0-√3
2x-√6y=0
√15x+√6y=0
(2+√15)x=0
therefore x=0,y=0
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