Solve the following system of equations by using the method of cross-multiplication: `2x+3y=17 ,\ \ \ \ 3x-2y=6`

Options

A. ` x = 4 , y = 2 `
B. ` x = - 4 , y = 2 `
C. ` x = 4 , y = 3 `
D. ` x = - 4 , y = 3 `

Answer

C

Explanation

The given equations may be written as
` 2x + 3y - 17 = 0 " " `… (i)
` 3 x - 2y - 6 = 0 " " `… (ii)
By cross multiplication , we hav

` therefore (x )/({ 3 xx (-6) - (-2 ) xx (-17)}) = ( y )/({ (-17) xx 3 - (-6) xx 2 } ) `
` " " = (1 )/({ 2 xx (-2) - 3 xx 3 })`
`rArr (x)/(( - 18 - 34)) = ( y ) /((- 51 + 12 )) = (1)/(( - 4 - 9))`
`rArr (x)/(-52) = (y ) /(-39) = (1)/( - 13)`
` rArr x = (-52)/(- 13) = 4 , y = (-39)/(-13) = 3 `
Hence, x = 4 and y = 3 is the required solution.