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Question

Find the solution of the given system of equations.

x+y82=x+2y148=3x+y1211


A

(1, -1)

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B

(2, 6)

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C

(2, 2)

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D

(0, 1)

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Solution

The correct option is B

(2, 6)


Take first two components,

x+y82=x+2y148

8(x+y8)=2(x+2y14)
8x+8y64=2x+4y28
6x+4y36=0

3x+2y18=0.....(i)

Take last two components,

x+2y148=3x+y1211

11(x+2y14)=8(3x+y12)

11x+22y154=24x+8y96

13x+14y58=0.....(ii)

On multiplying equation (i) by 7, we get

21x+14y126=0...(iii),

On subtracting equation (ii) from (iii), we get

34x=68

x=2

On substituting value of x=2 in equation (i), we get

3×2+2y18=0

y=6

The solution is (2, 6).


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