Question

write the following sentences as a system of inequalities in two variables. then graph the system. the sum of the x - variable and the y - variable is at most 2. the y - variable added to the product of 2 and the x - variable does not exceed 4. choose the correct system of inequalities. a. x + y ≥ 2 2x + y ≤ 4 b. x + y ≥ 2 2x + y ≥ 4 c. x + y ≤ 2 2x + y ≥ 4 d. x + y ≤ 2 2x + y ≤ 4

Explanation:

Step1: Translate first sentence

The sum of \(x\) and \(y\) is at most 2 means \(x + y\leq2\).

Step2: Translate second sentence

The \(y - \)variable added to the product of 2 and the \(x - \)variable does not exceed 4 means \(2x + y\leq4\).

Answer:

D. \(x + y\leq2\), \(2x + y\leq4\)