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Q. If $(x, y)$ is a variable point on the line $y=2 x$ lying between the lines $2(x+1)+y=0$ and $x+3(y-1)=0$, then

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Solution:

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Solving $y=2 x, 2(x+1)+y=0$, we get $x=-1 / 2, y=-1$. Solving $y=2 x, x+3(y-1)=0$, we get $x=3 / 7, y=6 / 7$.