Solve the system: y = e3x , and y = e2x-1Question 6Select one:a.(0, 1)b.(1/5, e3/5)c.(-1, e-3)d.No solutione.None of these

To solve the system of equations, we need to set the two equations equal to each other because they both equal y:

e^(3x) = e^(2x-1)

We can simplify this equation by taking the natural logarithm (ln) of both sides. This is because the natural logarithm and the exponential function are inverse operations, so they cancel each other out:

ln(e^(3x)) = ln(e^(2x-1))

This simplifies to:

3x = 2x - 1

Solving for x gives:

x = -1

Substituting x = -1 into the first equation y = e^(3x) gives:

y = e^(3*-1) = e^-3

So, the solution to the system of equations is (-1, e^-3), which corresponds to option c.