Problem

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

Solution

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 :\((2, -3)\)

From Solvely APP
Source: https://solvelyapp.com/problems/16172/

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