Chapter EP, Problem 10.7.8EP

To determine

To Find: The solution of the system of equations.

Answer to Problem 10.7.8EP

Thus, the solution of the equations is $\left(\frac{-3+\sqrt{30}}{7},\frac{4+\sqrt{30}}{7}\right)\left(\frac{-3-\sqrt{30}}{7},\frac{4-\sqrt{30}}{7}\right)$ ..

Explanation of Solution

Given:

The given equation are,

$\begin{array}{l}2{\left(x-1\right)}^2+5y^2=10\\ x-y=-1\end{array}$

Calculation:

Consider the given equation are,

$\begin{array}{l}2{\left(x-1\right)}^2+5y^2=10\\ x-y=-1\end{array}$

Consider the second equation is,

$x=y-1$

Substitute the above value in the first equation as,

$\begin{array}{l}2{\left(y-1-1\right)}^2+5y^2=10\\ 7y^2-8y-2=0\\ y=\frac{4\pm \sqrt{30}}{7}\end{array}$

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

$\begin{array}{l}\frac{4\pm \sqrt{30}}{7}-1=x\\ x=\frac{-3-\sqrt{30}}{7},\frac{4-\sqrt{30}}{7}\end{array}$

Thus, the solution of the equations is $\left(\frac{-3+\sqrt{30}}{7},\frac{4+\sqrt{30}}{7}\right)\left(\frac{-3-\sqrt{30}}{7},\frac{4-\sqrt{30}}{7}\right)$ .