Chapter 4.9, Problem 4LC

Solution

Solve the system by graphing.

  $(-1,4)and(-0.667,3.222)$

Given:

The given equation is, $\left\{\begin{array}{l}y>2x^2+x+3\\ y<-x^2-4x+1\end{array}\right.$

Concept Used:

• Solve the inequality for y.
• Graph the boundary line for the inequality.
• Shade the region that satisfies the inequality.
• Solve the second inequality for y.
• Graph the boundary line for the second inequality.
• Shade the region that satisfies the second inequality.

Calculation:

The given inequality is − $\left\{\begin{array}{l}y>2x^2+x+3\\ y<-x^2-4x+1\end{array}\right.$

The graph of given inequality is − $\left\{\begin{array}{l}y>2x^2+x+3\\ y<-x^2-4x+1\end{array}\right.$

  

  $(-1,4)and(-0.667,3.222)$

Thus, the solution of the given inequality is $(-1,4)and(-0.667,3.222)$ .