Solve the system: y = e3x , and y = 1/e.Question 40Select one:a.(1/3, e)b.(1/3, e-1)c.(–1/3, e-1)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.

So, we have e^(3x) = 1/e.

To solve for x, we can take the natural logarithm (ln) of both sides.

ln(e^(3x)) = ln(1/e)

Using the property of logarithms that allows us to bring down exponents, we get:

3x = ln(1/e)

To isolate x, we divide both sides by 3:

x = ln(1/e) / 3

The natural logarithm of 1/e is -1 (since e to the power of -1 equals 1/e), so:

x = -1/3

Substitute x = -1/3 into the first equation y = e^(3x) to solve for y:

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

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