Question

Solve for x,y:
(x+y-8)/2= (x+2y-14)/3 = (3x+y-12)/11
(class 10 CBSE SAMPLE PAPER 2017-18 MATHS)

Answer 1

SOLUTION:

(x+y-8)/2= (x+2y-14)/3 = (3x+y-12)/11


(x+y-8)/2……….(1)


(x+2y-14)/3………(2)


(3x+y-12)/11……..(3)


Take eq 1& 2


(x+y-8)/2= (x+2y-14)/3



3(x+y-8)= 2(x+2y-14)


3x+3y-24= 2x+4y-28


3x-2x+3y-4y= -28+24


x-y= -4


x-y+4=0…………….(3)


Take eq 2 & 3


(x+2y-14)/3 = (3x+y-12)/11


11 (x+2y-14)= 3(3x+y-12)


11x+22y - 154= 9x+3y-36


11x -9x+22y-3y= -36+154


2x+19y= 118


2x+19y-118=0…………….(4)


Multiply equation (3) by 2  


2x-2y+8=0………..(5)


subtract equation (4) from eq (5)


2x-2y+8=0

2x+19y-118=0

(-)   (-)   (+)

_________________

-21y+126=0


-21y=-126


y= 126/21= 6


y= 6


From eq 3


x+y -8=0


x+6-8=0


x-2=0


x=2


Hence, the value of x= 2 & y= 6


Hope this will help you....

Answer 2

Hope this will help....with verification