Chapter 9.7, Problem 7OE

To determine

To calculate: To find the number of real solutions of system of equations

Answer to Problem 7OE

Number of real solutions is $1$

Explanation of Solution

Given information: System of equations $x^2-y^2=4;x+y=2$

Calculation:

Given the system of equations as follows:

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

From equation (2):

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

Substituting the value in equation (1):

  $\begin{array}{l}{x}^2-{\left(2-x\right)}^2=4\\ x^2-4-x^2+4x=4\\ 4x=8\\ x=2\end{array}$

When $x=2$

  $\begin{array}{l}{2}^2-y^2=4\\ 4-y^2=4\\ y^2=0\\ y=0\end{array}$

Thus, solution is $\left(2,0\right)$

Conclusion:

Hence, number of real solutions is $1$