Sir please give me a detailed solution of this question as it was already asked in various important examinations in which we have given two equations x/6+y/15=4, x/3-y/12=19/4 and we have to find the value of variables x and y by using the method of cross multiplication

RS Aggarwal, Class 10, chapter 3C, question no 8

## Simplify given equations:

x/6+y/15=4

(5x+2y)/30=4

5x+2yâˆ’120=0

AndÂ x/3âˆ’y/12=19/4

4xâˆ’yâˆ’57=0

New set of equation is:

5x+2yâˆ’120=0....(1)

4xâˆ’yâˆ’57=0....(2)

From equationÂ (1):a1â€‹=5,b1â€‹=2Â andÂ c1â€‹=âˆ’120

From equationÂ (2):a2â€‹=4,b2â€‹=âˆ’1Â andÂ c2â€‹=âˆ’57

Using cross multiplication

x/(âˆ’114âˆ’120)=y/(âˆ’480+285â€‹)=1/(âˆ’5âˆ’8)â€‹

x/âˆ’234=y/âˆ’195â€‹=1/âˆ’13â€‹

x/âˆ’234â€‹=1/âˆ’13â‡’x=âˆ’234/-13â€‹

â‡’x=18

And

y/âˆ’195â€‹=1/âˆ’13â€‹

OrÂ y=15

AnswerÂ x=18Â andÂ y=15