Question

33.
If 6x + 7y = 2004 and 7x + y = 4002, then x + y = equals
यदि 6x +7y = 2004 और 7x + 6y = 4002, तब x + y का मान होगा -
(A) 400
(B) 462
(C) 487
(D) 770
​

Answer 1

{6x+7y=2004........(I)}×7

{7x+6y=4002.......(II)}×6

multiplying eq(I) by 7 and eq(II) by 6,,

on substracting them,,

42x+49y=14028

_42x+_36y=_24012

________________

13y=9984

y=9984/13

y=768

now,,,the value of y putting on eq(I),

then,,

$6x + 7y = 2004 \\ = > 6x + 7 \times 768 = 2004 \\ = > 6x + 5376 = 2004 \\ = > 6x = 2004 - 5376 \\ = > 6x = - 3372 \\ = > x = \frac{ - 3372}{6} \\ = > x = - 562$

Hence,, the value of,

x+y=-562+768

=206

Hope it helps you...

Answer 2

Given, $6x + 7y = 2004$ ....(1)and $7x + y = 4002$

$7x + y = 4002\\\Rightarrow 49x+7y=28014$...(2)

Subtracting (1) from (2)

$43x=26010\Rightarrow x=\frac{26010}{43}=604\frac{38}{43}\\\therefore 7x+y = 6x+(x+y)=4002=6\frac{26010}{43}\\\Rightarrow x+y=4612\frac{38}{43}$

Similarly, $6x + 7y = 2004$...(1) and $7x + 6y = 4002$...(2)

Adding (1) and (2)

$13x+13y=6006\\\Rightarrow x+y=462$

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