congrats!!! i followed and enjoyed every problem of this blog last year. i used to persevere with those problems. hoping to get problems of that level and sheen this year also.
subtracting eqn. 2 from 1 , 3 from 2 and 4 from 3,we get x-2y=-1 , 2y-3z=-1 , 3z-4w=-22 => x = 4w+24.
now, multipling eqn. 1 by 2 and adding it with eqn. 2 5(x+y) + 3z + 3w = 4. substituting the value of x+y from eqn. 3, we get 17z+2w=11 now solving the two eqns. in z and w. we get z and x and hence can obtain the values of other variables also.
congrats!!!
ReplyDeletei followed and enjoyed every problem of this blog last year. i used to persevere with those problems. hoping to get problems of that level and sheen this year also.
i m getting w=19/7
i.e. (5)
correct me if i m wrong
Thanks!
ReplyDeleteThe answer is incorrect
now i got it!
ReplyDeletex=-2 , z=0 , y=-1/2 and w=11/2
right!! post the process :)
ReplyDeletesubtracting eqn. 2 from 1 , 3 from 2 and 4 from 3,we get
ReplyDeletex-2y=-1 , 2y-3z=-1 , 3z-4w=-22
=> x = 4w+24.
now, multipling eqn. 1 by 2 and adding it with eqn. 2
5(x+y) + 3z + 3w = 4.
substituting the value of x+y from eqn. 3, we get
17z+2w=11
now solving the two eqns. in z and w. we get z and x
and hence can obtain the values of other variables also.
the symmetry is too close to neglect, multiplying the equations by 12, 6, 4, 3 resp. and adding will give the value of x+y+z+w
ReplyDelete