I can solve a system of linear equations by adding

Junaid Ayala

Junaid Ayala

Answered question

2022-02-18

I can solve a system of linear equations by adding the constituent equations together or subtracting them from one another (via the so-called "elimination" method), but can one do the same with a system of linear inequalities. In other words, is an operation of the following form valid?
x>b,a>b Therefore
x+a>y+b

Answer & Explanation

mapogoosae

mapogoosae

Beginner2022-02-19Added 4 answers

Yes, it is valid. You can prove it's validness in two steps: First, if a<b then a+x<b+x.
Secondly, if x<y then 0<yx, by adding x to both sides.
Hence b+x<b+x+yx=b+y.
Finally, a+x<b+y

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