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Question

If 2x+y+25=3x-y+13=3x+2y+16 then
(a) x = 1, y = 1 (b) x = − 1, y = − 1 (c) x = 1, y = 2 (d) x = 2, y = 1

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Solution

Consider 2x+y+25=3x-y+13 and 3x-y+13=3x+2y+16. Now, simplifying these equations, we get
32x+y+2=53x-y+16x+3y+6=15x-5y+59x-8y=1 .....i
And
63x-y+1=33x+2y+118x-6y+6=9x+6y+33x-4y=-1 .....ii
Multiplying (ii) by 2 and subtracting it from (i)
9x-6x=1+2x=1
Now, putting x = 1 in (ii), we have
3×1-4y=-1y=3+14=1
Thus, x = 1, y = 1.
Hence, the correct answer is option (a).

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