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In the given diagram the co-ordinates of B and C are $(-2,-1)$ and $(-2,8)$enter image description here respectively. The shaded region inside the $\triangle ABC$ represented by three inequalities. One of these is $x + y <=6$. Write down the co-ordinates of A and other two inequalities. Also calculate the maximum value of $x +2y$ from the values which satisfy all three inequalities.

Actually I thought about it too much but couldn't get enough idea to start. Can anyone help me?

Help much appreciated

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One of the inequalities is $x+y <= 6$, which means one of the sides of the triangle is given by the line $x+y=6$; you should be able to use this and the points B and C to solve for A.

After this, you know the other two inequalities define the other two sides, and you can infer them the same way we inferred one of the sides from $x+y <= 6$.

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