My question is : Solve simultaneously-
{|x−1|+|y−2|=1y=3−|x−1|
I tried to solve this question by the method told by Marvis as I had understood that method (its here: Solve an absolute value equation simultaneously
But the solution set i got for the above question is not correct.
My solution was: y≥2, and x=3 or x=y-2.
I would like to know the final correct solution.
Answer
We shall proceed on similar lines as the answer here.
You have that |x−1|+|y−2|=1. This gives us that |x−1|=1−|y−2|.
This gives us that y−|y−2|=2.
If y>2, then we get that y−y+2=2,
If y≤2, then we get that y+y−2=2⟹y=2
Since |x−1|≥0, we need 3−y≥0
If x≥1, then x−1=3−y⟹x=4−y. Note that since y∈[2,3], x=4−y≥1.
If x<1, then x−1=y−3⟹x=y−2. Note that since y∈[2,3], x=y−2<1.
Hence, the solution set is given as follows. 2≤y≤3 and x=4−y or y−2
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