Answer
See the explanation below.
Work Step by Step
Step 1: Make the either equation in the form of $y^2$ in order to this will multiply either equation by $2$.
Step 2: After this, add the original equation and new equation.
Step 3: We will get the solution in only one variable.
Step 4: we will solve for the value of the either $x$ or $y$ variable that satisfies the equation.
Step 5: Finally, we will get the solution set in the form of $(x,y)$
Let us take an example: After adding the given two equations, we get $\dfrac{11}{x^2}=11$ when we multiply the first equation by $2$.
or, $x^2=1$;
or $x=\pm 1$
From first equation $\dfrac{6}{x^2}+\dfrac{2}{y^2}=14$ when $x=1$, we have $y=\pm \dfrac{1}{2}$
From first equation $\dfrac{6}{x^2}+\dfrac{2}{y^2}=14$ when $x=-1$, we have $y=\pm \dfrac{1}{2}$
Thus, solution set is {$(1,\dfrac{1}{2}),(1,-\dfrac{1}{2}),(-1,\dfrac{1}{2}),(-1,-\dfrac{1}{2})$}
