Chapter EP, Problem 10.7.7EP

To determine

To Find: The solution of the system of equations.

Answer to Problem 10.7.7EP

Thus, the solution of the equations is $\left(\pm \sqrt{15},2\right)\left(\pm \sqrt{111},10\right)$ ..

Explanation of Solution

Given:

The given equation are,

$\begin{array}{l}4x^2-3{\left(y+2\right)}^2=12\\ x^2-y^2=11\end{array}$

Calculation:

Consider the given equation are,

$\begin{array}{l}4x^2-3{\left(y+2\right)}^2=12\\ x^2-y^2=11\end{array}$

Consider the second equation is,

$x^2=11+y^2$

Substitute the above value in the first equation as,

$\begin{array}{l}4\left(11+y^2\right)-3{\left(y+2\right)}^2=12\\ 44+4y^2-3y^2-12y-12=12\\ y^2-12y+20=0\\ y=2,10\end{array}$

Substitute the values of $y$ in the second equation as,

$\begin{array}{l}{x}^2=11+{\left(2\right)}^2,11+{\left(20\right)}^2\\ x=\pm \sqrt{15},\pm \sqrt{111}\end{array}$

Thus, the solution of the equations is $\left(\pm \sqrt{15},2\right)\left(\pm \sqrt{111},10\right)$ .