Chapter 16.3, Problem 1MRE

To determine

To evaluate: the real solutions of the system.

Answer to Problem 1MRE

The system has no real solutions.

Explanation of Solution

Given:

Consider the system of equation.

  $\begin{array}{l}2x^2+y^2=5\\ x^2=1-y^2\end{array}$

Calculation:

Consider the given system.

  $\begin{array}{l}2x^2+y^2=5\mathrm{......}(1)\\ x^2=1-y^2\mathrm{......}(2)\end{array}$

Substitute equation (2) in equation (1).

  $\begin{array}{c}2\left(1-y^2\right)+y^2=5\\ 2-2y^2+y^2=5\\ 2-y^2=5\\ y^2=-3\end{array}$

As square of any real number can’t be negative.

So, there is no real value for $y$ .

Substituting the value of ‘ y’ in equation (2),

  $\begin{array}{l}{x}^2=1-y^2\\ x^2=1+3\\ x^2=4\\ x=\pm 2\end{array}$

So, the solution of the given equations is not real.