What's the locus of the intersection of these variable lines?

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The line \(x+y=t\) meets the line \(y=tx\) at the point \(P\). Find the coordinates of \(P\) in terms of \(t\). Hence, or otherwise, show that the equation of the locus of \(P\) as \(t\) varies is \(x^2+xy-y=0\). At the point on the locus where \(x=3\), find the value of \(y\) and the value of \(t\).