Region given by these inequalities in XY Plane

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Given region as $ 0\leq x \leq y $ , $ x+y \leq 1$ . I did this as enter image description here

Is this correct ?

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Your sketch is correct. The intercepts are both 1, if you want to label those.

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Yes, you are correct. Find the bounds of the region by converting the inequalities to equalities. Here is a plot of the solution using wolfram alpha: enter image description here