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Question

If 3x+y+2x-y=2 and 9x+y-4x-y=1 then
(a) x=12, y=32          (b) x=52, y=12          (c) x=32, y=12          (d) x=12, y=52


Solution

The given equations are
3x+y+2x-y=2                                        .....i9x+y-4x-y=1                                        .....ii
Substituting 1x+y=u and 1x-y=v in (i) and (ii), the new system becomes
3u+2v=2                                                    .....iii9u-4v=1                                                    .....iv
Now, multiplying (iii) by 2 and adding it with (iv), we get
6u+9u=4+1u=515=13
Again, multiplying (iii) by 3 and subtracting (iv) from it, we get
6v+4v=6-1v=510=12 
Therefore
x+y=3                                                          .....vx-y=2                                                          .....vi
Adding (v) and (vi), we get
2x=3+2x=52
Substituting x=52, in (v), we have
52+y=3y=3-52=12
Thus, x=52 and y=12.
Hence, the correct answer is option (b).

Mathematics
RS Aggarwal (2018)
Standard X

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