Question

Solve the system of two linear inequalities graphically. Find the region with points that satisfy both inequalities.(Select the region you wish to be shaded?)

Answer 1

Explanation:

Given the following system of inequalities

`\begin{gathered} 5x\text{ }+\text{ 2y }<\text{ -20} \\ x\text{ }\ge\text{ -5} \\ \text{ We will n}eed\text{ to solve the inequality one after the other} \\ \text{Given that; 5x + 2y < -20} \\ \text{Step 1: Convert the inequality to an equation} \\ We\text{ have; 5x + 2y = -20} \\ \text{ Find x and y by isolating each of the variable} \\ To\text{ find x let y = 0} \\ 5x\text{ + 2(0) = -20} \\ 5x\text{ + 0 = -20} \\ 5x\text{ = -20} \\ \text{Divide both sides by 5} \\ (5x)/(5)\text{ = }(-20)/(5) \\ x\text{ = -4} \\ To\text{ find y, let x = 0} \\ 5x\text{ + 2y = -20} \\ 5(0)\text{ + 2y = -20} \\ 0\text{ + 2y = -20} \\ 2y\text{ = -20} \\ \text{Divide both sides by }2 \\ (2y)/(2)\text{ = -20/2} \\ y\text{ = -10} \\ \text{Hence, we have (-4, -10) for the inequality expression }5x\text{ + 2y < -20} \end{gathered}`

The next step is to graph the following point

Hence, the answer isopti D