Question

Choose the point whose coordinates lie within the region given by thefollowing system of inequalities.y> 2x + 3y<-3x-1 A. (-1,-4)B. (-4,1)C. (-1,4)D. (1,4)

Answer 1

Solution

Step 1

y > 2x + 3

$\begin{gathered} \text{ y = 2x + 3} \\ find\text{ x when y = 0} \\ 0\text{ = 2x + 3} \\ x\text{ = }\frac{-3}{2} \\ (\frac{-3}{2},0) \\ find\text{ y when x = 0} \\ \\ y\text{ = 2}\times0\text{ + 3} \\ y\text{ = 3} \\ (0,\text{ 3\rparen} \end{gathered}$

Step 2

y < -3x-1

$\begin{gathered} y\text{ = =3x-1} \\ find\text{ y when x = 0} \\ \\ y\text{ = -3}\times0\text{ - 1} \\ y\text{ = -1} \\ (0,\text{ -1\rparen} \\ \\ Find\text{ x when y = 0} \\ 0\text{ = -3x - 1} \\ x\text{ = }\frac{-1}{3} \\ (\frac{-1}{3},0) \end{gathered}$

Step 3

Use all the coordinates to graph the inequalities

Final answer

B. (-4, 1)