Solve the system by the method of substitution. $$\{\begin{array}{rl}{x}^2-12y^2& =144\\ x^2+y^2& =1\end{array}$$

A) $(0,12),(0,-12)$
B) $\left(12,\frac{1}{12}\right),\left(12,-\frac{1}{12}\right),\left(-12,\frac{1}{12}\right),\left(-12,-\frac{1}{12}\right)$
C) (12 $2\sqrt{3}$ , 12 $\sqrt{13}$ ) , (12 $2\sqrt{3}$ , 12 $\sqrt{13}$ ) , ( 12 $2\sqrt{3}$ ,12 $\sqrt{13}$ ) , ( 12 $2\sqrt{3}$ , 12 $\sqrt{13}$ )
D) $\left(\frac{155}{11},-\frac{144}{11}\right)$
E) no solution exists

Method of Substitution

A technique for solving systems of equations where one of the equations is solved for one variable in terms of the others, and then substituted into the other equation(s).

System of Equations

A set of equations with the same variables, which are solved together to find the values of these variables.