SOLUTION: Which of the following is a linear constraint? 5y + 3x2 ≥ 33 17x + 3xz ≤ 4 7x ≤ 3xy + 14z - 12 3x ≥ 14y + 2z + 13

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Question 1113555: Which of the following is a linear constraint?
5y + 3x2 ≥ 33
17x + 3xz ≤ 4
7x ≤ 3xy + 14z - 12
3x ≥ 14y + 2z + 13
Found 2 solutions by greenestamps, solver91311:
Answer by greenestamps(13200)   (Show Source): You can put this solution on YOUR website!


"Linear" means each variable appears by itself, and only to the first power. Stated differently, each term is either a constant (no variables) or contains a single variable to the first power.

5y + 3x2 ≥ 33 no; can't have an x^2 term
17x + 3xz ≤ 4 no; can't have a term with the product of two variables
7x ≤ 3xy + 14z - 12 ditto
3x ≥ 14y + 2z + 13 yes!
Answer by solver91311(24713)   (Show Source): You can put this solution on YOUR website!


In order to be a linear constraint, all of the terms must be linear or constant. A linear term is one where the sum of the exponents on the variables in the term is 1 and a constant term is where the sum of the exponents on the variables is 0. If a term has no visible variables, you can assume as many variables as you like are there so long as all of the exponents are zero. If you see a variable without an exponent, you can assume an exponent of 1 on that variable. Symbolically: no matter what is. And

Examples:

A constant term, aka a term of degree 0:



A linear term, aka a term of degree 1. Note the sum of the exponents is 1:



A non-linear term, in this case a term of degree 2. Note the sum of the exponents is 2:





John

My calculator said it, I believe it, that settles it
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