Solve the following system of equations by elimination method:

√2x – √3y = 0

√5x + √2y = 0

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.