System

find the value of k for which the system of equations has a unique solution 2x+ky-9=0 , kx+3y-13=0. ​

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2x+ky-9=0 , kx+3y-13=0  ​

\(y=(-2x+9)/k\\ y=(-kx+13)/3\)

The system of equations has unique solutions for many values of k.

 \(k\in \{\) \(-1,\)   \(4,\)    \(5,\)  \(etc.\ \}\)

 \(x\in \{\) \(\ 8,\)    \(2.5,\)  \(2\}\)

 \(y\in \{\) \(\ 7,\)     \(1,\)     \(1\}\)

  !