Q:

Write a system of inequalities to represent the shaded portion of the graph.

Accepted Solution

A:
Answer:The solution of the system of inequalities 3x > y and x + y ≤ 4 is graphed by the shaded region given.Step-by-step explanation:See the graph attached. The dotted straight line passes through the points (0,0) and (3,1). Therefore, the equation is [tex]\frac{y - 0}{0 - 1} = \frac{x - 0}{0 - 3}[/tex] {Using the two point form of equation of straight line} ⇒ 3y = x ........ (1) Therefore, the shaded part of the graph holds the equation 3y > x {AS the shaded portion does not include the straight line (1)}Again, the equation of the firm line is given by [tex]\frac{x}{4} + \frac{y}{4} = 1[/tex] {Applying the intercept form of equation of straight line} ⇒ x + y = 4 ......... (2) Therefore, the shaded region of the graph is represented by the equation  x + y ≤ 4 {Since, the shaded region includes the line also} Therefore, the solution of the system of inequalities 3x > y and x + y ≤ 4 is graphed by the shaded region given. (Answer)