Solve for ` x and y ` :
` ( 3x )/( 2) - ( 5y )/( 3) = - 2, ( x)/(3) + ( y)/(2) = (13)/(6)`

Options

A. `(3,2)`
B. `(2,3)`
C. `(2,4)`
D. `(4,2)`

Answer

B

Explanation

The given system of equations may be written as
` 9x - 10 y + 12 = 0 " " ` … (i)
` 2x + 3y - 13 = 0 " " `… (ii)
From (ii) we get `y = (13 - 2x )/( 3 )`
Substituting `y = ( 13 - 2x )/(3 )` in (i), we get
`9x - (10 (13 - 2x ))/(3) + 12 = 0 `
`rArr 27x - 10 ( 13 - 2x ) + 36 = 0 `
` rArr 27 x - 130 + 20 x + 36 = 0 `
`rArr 47 x - 94 = 0 rArr 47 x = 94 rArr x = (94)/( 47 ) = 2`.
Substituting ` x = 2 `in (i), we get
` 9 xx 2 - 10 y + 12 = 0 rArr 10 y = 30 rArr y = (30)/( 10 ) = 3.`
Hence, ` x = 2 and y = 3 ` is the required solution.