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Look at 15 high school math meeting questions.
Let 2x-y=t, then 2x-y-t=0,

The distance from the center of the circle (-1, 2) to the straight line does not exceed the radius, so | 2 *( 1)-2-t |/√5.

So | t+4 |

The solution is -4-2 √ 5.

That is, the maximum value of 2x-y is -4+2√5.