Solve the following by using cross multiplication method ` 4x - 7y + 28 = 0 , 5y - 7 x + 9 = 0 `

Options

A. `x = 4` and `y = 5`
B. `x = 5` and `y = 6`
C. `x = 6` and `y = 7`
D. `x = 7` and `y = 8`

Answer

D

Explanation

The given equations are
`4x - 7y + 28 = 0 " " `…(i)
` - 7x + 5y + 9 = 0 " " `… (ii)
By cross multiplication , we have

` therefore (x)/({(- 7 )xx 9 - 5 xx 28}) = (y)/( { 28 xx (-7) - 9xx 4} ) = (1)/({ 4xx 5 - (-7) xx (-7)})`
` rArr (x)/(( - 63 - 140)) = (y )/(( - 196 - 36)) = (1)/(( 20 - 49)) `
`rArr (x)/(-203) = ( y )/(-232) = (1)/(-29)`
`rArr x = ((-203)/(-29)) = 7 and y = (( - 232)/(- 29)) = 8`
Hence, x = 7 and y = 8 is the required solution.