Solve: \( \left\{\begin{array}{l}2 x^{2}-6 y^{2}=-78 \\ x^{2}+3 y^{2}=51\end{array}\right. \)

Step 1 ：\( x^{2} = 51 - 3y^{2} \)

Step 2 ：\( 2(51 - 3y^{2}) - 6y^{2} = -78 \)

Step 3 ：\( y^{2} = 22, y = \pm \sqrt{22} \)

Step 4 ：\( x = \pm \sqrt{51 - 66} = \pm \sqrt{-15} \)