35. Which system of equations has the same solution as the system below? \[ \begin{array}{l} 2 x+2 y=16 \\ 3 x-y=4\end{array} \] \( \begin{array}{rr}2 x+2 y=16 & \text { B. } \begin{aligned} 2 x+2 y & =16 \\ 6 x-2 y & =8 \\ 6 x-2 y & =4\end{aligned} \\ \begin{array}{rr}x+y & =16\end{array} & \text { D. } \begin{array}{l}6 x+6 y \\ \text { A. } \\ 6 x+2 y\end{array} \\ 3 x-y=4\end{array} \)

To find a system of equations that has the same solution, we need to manipulate the original equations through addition, multiplication, or substitution without changing their solution set. For instance, if we multiply the entire second equation \(3x - y = 4\) by 2, we get \(6x - 2y = 8\). Now, both equations are \(2x + 2y = 16\) and \(6x - 2y = 8\), which will yield the same solutions as the original system. Don't forget to check if the new system is formed correctly. A common mistake is to alter the constants or coefficients without keeping the relationships of the variables intact. Always simplify or scale equations with the intention of maintaining equality and check the solution set with substitution or graphing methods if necessary!