Determine if the solutioir set for the system of equations shown is the empty set, contains one point or is infinite.
\[
\begin{array}{l}
x-y=5 \\
2 x+y=1
\end{array}
\]
0
1 solution
Infinite

Answer

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Answer

\((2, -3)\)

Steps

Step 1 ：\(\begin{cases} x-y=5\\ 2x+y=1 \end{cases}\)

Step 2 ：\(\begin{cases} x-y=5\\ 2x+y=1 \end{cases} \Rightarrow \begin{cases} x=y+5\\ 2x+y=1 \end{cases}\)

Step 3 ：\(\begin{cases} x=y+5\\ 2(y+5)+y=1 \end{cases} \Rightarrow y = -3\)

Step 4 ：\(x = -3 + 5 \Rightarrow x = 2\)

Step 5 ：\((2, -3)\)