Chapter 9.9, Problem 4ST

To determine

To calculate: To solve the system of equations

Answer to Problem 4ST

Solutions are $\left(0,5\right),\left(0,-5\right)$

Explanation of Solution

Given information: System of equations $25x^2+16y^2=400;x^2+y^2=25$

Calculation:

Given the system of equations as follows:

  $\begin{array}{l}25x^2+16y^2=400-----(1)\\ x^2+y^2=25--------(2)\end{array}$

From equation (2),

  $y^2=25-x^2$

Substituting the values in (1):

  $\begin{array}{l}25x^2+16\left(25-x^2\right)=400\\ 25x^2+400-16x^2=400\\ 9x^2=0\\ x^2=0\\ x=0\end{array}$

When $x=0$

  $\begin{array}{l}{y}^2=25-0\\ y^2=25\\ y=\pm 5\end{array}$

Conclusion:

Hence, solutions are $\left(0,5\right),\left(0,-5\right)$