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 7. the y-variable added to the product of 4 and the x-variable does not exceed 8. choose the correct system of inequalities. a. x+y ≤ 7, 4x+y ≤ 8; b. x+y ≤ 7, 4x+y ≥ 8; c. x+y ≥ 7, 4x+y ≤ 8; d. x+y ≥ 7, 4x+y ≥ 8

Explanation:

Step1: Analyze first sentence

"The sum of the x - variable and the y - variable is at most 7" means \(x + y\leqslant7\) (since "at most" implies less than or equal to).

Step2: Analyze second sentence

"The y - variable added to the product of 4 and the x - variable does not exceed 8" means \(4x + y\leqslant8\) (since "does not exceed" implies less than or equal to).

Step3: Match with options

Looking at the options, option A has \(x + y\leqslant7\) and \(4x + y\leqslant8\), which matches our derived inequalities.

Answer:

A. \(x + y\leqslant7\); \(4x + y\leqslant8\)