Chapter 9.7, Problem 28PPS

To determine

To find: The solution for the given system of the equation.

Answer to Problem 28PPS

The common region of the Figure 2 shows the solution of the inequalities.

Explanation of Solution

Given:

The given system of equation is,

  $\begin{array}{l}-x>y^2\\ 4x^2+14y^2\le 56\end{array}$

Calculation:

Consider the given equation are,

  $\begin{array}{l}-x>y^2\\ 4x^2+14y^2\le 56\end{array}$

The graph for the above two equation is shown in Figure 1

  

Figure 1

The inequality $-x>y^2$ is more than the sign point $\left(0,2\right)$ from the exterior of the parabola does not satisfy the inequality. The region inside the parabola will satisfy the inequality.

The inequality $4x^2+14y^2\le 56$ has less than and equal to sign. Point (0,0) from the interior of the ellipse satisfies the inequality. The region that is interior of the ellipse and on the boundary of the ellipse that satisfy the inequality.

Thus, the solution for the inequalities is shown in Figure 2

  

Figure 2

The common region represents the solution of the system.