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For each of the following equations, explain why it is or is not linear.

a. 2X - 3Y > 12

b. X2 + Y2 < 100

c. 1.5X - XY > 0

d. 1500X + 200Y + 1000Z > 7500

e. 2000X &#8805; 1500Z + 750

https://brainmass.com/math/linear-algebra/explain-following-equation-not-linear-165161

SOLUTION This solution is FREE courtesy of BrainMass!

For each of the following equations, explain why it is or is not linear.
Following are the conditions of linearity based on which we decide whether an equation is linear or not.
Linearity means no roots, powers, radicals, reciprocals, or ratios
Products represented in the objective function are fully independent of one another
a. 2X - 3Y > 12
This equation is linear as all the variables have power of 1.

b. X2 + Y2 < 100
Assuming that this equation is X2 + Y2 <100, it is not linear because it contains 2 terms with power of 2. This is a violation of linearity condition of no powers.

c. 1.5X - XY > 0
This equation is not linear as it contains one term resulting in power of 2(XY). This is a violation of linearity condition of no powers.

d. 1500X + 200Y + 1000Z > 7500
This equation is linear as all the variables have power of 1.

e. 2000X ≥ 1500Z + 750
This equation can also be written as: 2000X-1500Z>=750
This is a linear equation as all the variables have power of 1.

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