Solving Linear System with inequalities. <mtable columnalign="right left right left right left r

drarvoihootg2k4o

drarvoihootg2k4o

Answered question

2022-06-03

Solving Linear System with inequalities.
b x = 0 a 0.33 b 0.5 x = 0 d 0.33 b = 0 a 0.33 b + c = 0 a + b + c + d + 2 x = 1 a + b + c + d 8.8 x 0 a + b + c + d 7.27 x 0
where a,b,c,d and x are unknown variables.
Is there any solution to this system and how to solve this system?

Answer & Explanation

bapeSoypelp0vs

bapeSoypelp0vs

Beginner2022-06-04Added 4 answers

Since
x = b
d = 0.33 b
a = 0.33 b + 0.5 b = 0.83 b
c = 0.33 b 0.83 b = 0.5 b
one has
1 = ( 0.83 + 1 0.5 + 0.33 + 2 ) b b = 1 3.66
Hence,
a = 0.83 3.66 , b = 1 3.66 , c = 0.5 3.66 , d = 0.33 3.66 , x = 1 3.66 .
However,
a + b + c + d 7.27 x = 0.83 + 1 0.5 + 0.33 7.27 3.66 = 5.61 3.66 < 0
so, the system has no solution.
Thalia Ortiz

Thalia Ortiz

Beginner2022-06-05Added 1 answers

Some hints:
1. b x = 0, and thus b = x.
2. Now we have a 0.5 x 0.33 b = 0, thus a 0.5 x 0.33 x = 0, thus a 0.83 x = 0, and thus a = 0.83 x.
3. What do we know of d in the form of b?

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