Fif in the blanks so that the resulting statement is true When solving $\left\{\begin{array}{l}3 x^{2}+2 y^{2}=35 \\ 6 x^{2}+3 y^{2}=47\end{array}\right.$ by the addifion method, we can eliminate $x^{2}$ by multiplying the first equation by and then adding the equations.

Step 1 ：The addition method involves manipulating the equations such that when they are added together, one of the variables cancels out. In this case, we want to eliminate \(x^{2}\). To do this, we need to make the coefficients of \(x^{2}\) in both equations equal so that they cancel out when the equations are added together.

Step 2 ：The coefficient of \(x^{2}\) in the first equation is 3 and in the second equation is 6. If we multiply the first equation by 2, the coefficient of \(x^{2}\) in the first equation becomes 6, which is equal to the coefficient of \(x^{2}\) in the second equation.

Step 3 ：Therefore, we should multiply the first equation by 2.

Step 4 ：Final Answer: We should multiply the first equation by \(\boxed{2}\).