4. (a) The curves \(\mathrm { e } ^ { x } - 2 \mathrm { e } ^ { y } = 1\) and \(2 \mathrm { e } ^ { x } + 3 \mathrm { e } ^ { 2 y } = 41\) intersect at the point \(P\). Show that the \(y\)-coordinate of \(P\) satisfies the equation \(3 \mathrm { e } ^ { 2 y } + 4 \mathrm { e } ^ { y } - 39 = 0\).
(b) In this question you must show detailed reasoning. Hence find the exact coordinates of \(P\).
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