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)
\[
\begin{array}{l}
9 x+9 y=22 \\
18 x+9 y=45
\end{array}
\]

Answer

Expert–verified

Hide Steps

Answer

\[ \Rightarrow \boxed{\text{(C)}} \]

Steps

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 ：\[ \Rightarrow \boxed{\text{(C)}} \]