# explain why following equation is or is not linear.

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 ≥ 1500Z + 750

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## 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 â‰¥ 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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