linear equation with dos variables

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raven2k7

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hi everyone, so i have a question, i was given this linear equation in the image uploaded. and the other image shows my working. now i know that the points cross at (1,1)
. that part that confuses me is that in the book it mentions that (-1,2) and (-2,1) belong to the shaded area. now i know that they obtained (-1,2) by this y= -x+2 = 1=-1+2
but can someone explain to me how they got the (-2,1) ? thanks

images are uploaded
 

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raven2k7 said:
hi everyone, so i have a question, i was given this linear equation in the image uploaded. and the other image shows my working. now i know that the points cross at (1,1)
. that part that confuses me is that in the book it mentions that (-1,2) and (-2,1) belong to the shaded area. now i know that they obtained (-1,2) by this y= -x+2 = 1=-1+2
but can someone explain to me how they got the (-2,1) ? thanks (images are uploaded)
Click to expand...

You drew the line x+y = 2 and from there you drew shaded the region \(\displaystyle \ \ x+y \le \ 2 \ \)below the line (x+y = 2)

Correct.

When x=-2, on the line (x+y = 2) we have y = 4 and (-2,4) is on the line.

So (-2,1) will be below the line (because 1<4) - in the shaded region.
 
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