Problem
Which system of equations has the same solution as the system below? \[ \begin{array}{l} 3 x+3 y=8 \\ 2 x-y=5 \end{array} \] (A) \[ \begin{array}{l} 3 x+3 y=8 \\ 4 x-2 y=5 \end{array} \] (B) \[ \begin{array}{l} 3 x+3 y=8 \\ 4 x-2 y=10 \end{array} \] (C) \[ \begin{array}{l} x+y=8 \\ 2 x-y=5 \end{array} \] (D) \[ \begin{array}{l} 9 x+9 y=22 \\ 18 x+9 y=45 \end{array} \]
Solution
Step 1 ：\[ \frac{1}{3} (3 x + 3 y)=\frac{1}{3} (8) \Rightarrow x+y= \frac{8}{3} \]
Step 2 ：\[ \begin{array}{l} x+y=\frac{8}{3} \\ 2 x-y=5 \end{array} \]
Step 3 ：\[ \Rightarrow \boxed{\text{(C)}} \]
