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\[ 4x + x = 2 - 6 \]
\[ 5x = -4 \]
\[ x = -\frac{4}{5} \]
Substitute \(x = -\frac{4}{5}\) into \(y = 2x + 3\):
\[ y = 2\left(-\frac{4}{5}\right) + 3 = -\frac{8}{5} + \frac{15}{5} = \frac{7}{5} \]
Thus, the intersection point is \(\left(-\frac{4}{5}, \frac{7}{5}\right)\).
\(\boxed{\left(-\frac{4}{5}, \frac{7}{5}\right)}\)
An entomologist simplifies a complex ratio of wingbeat frequencies given by \(\frac{3 + \sqrt{5}}{2 - \sqrt{5}}\). Rationalize the denominator and express in simplest form.
Multiply numerator and denominator by the conjugate of the denominator \(2 + \sqrt{5}\):
\[ \frac{3 + \sqrt{5}}{2 - \sqrt{5}} \cdot \frac{2 + \sqrt{5}}{2 + \sqrt{5}} = \frac{(3 + \sqrt{5})(2 + \sqrt{5})}{(2 - \sqrt{5})(2 + \sqrt{5})} \]