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Question

Let α=(x+4y)a+(2x+y+1)b and β=(y2x+2)a+(2x3y1)b where a and b are non-zero, non-collinear. If 3α=2β then

A
x=1,y=2
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B
x=2,y=1
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C
x=1,y=2
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D
x=2,y=1
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Solution

The correct option is D x=2,y=1
α=(x+4y)a+(2x+y+1)b and β=(y2x+2)a+(2x3y1)b
3α=2β
3(x+4y)=2(y2x+2) and 3(2x+y+1)=2(2x3y1)
7x+10y4=0 and 2x+9y+5=0
solving above two equations gives x=2 and y=1
Hence, option D.

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