Problem

Question 3 (1 point)
Solve the linear-exponential system of equations by graphing on your own paper. Express your values as decimals rounded to the nearest hundredth, if necessary.
\[
\begin{array}{l}
y=0.6 x-4.3 \\
y=(x-5)^{2}-1
\end{array}
\]

Answer

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Answer

\(\boxed{\text{The system of equations has no real solutions.}}\)

Steps

Step 1 :Set the two equations equal to each other: \(0.6x - 4.3 = (x - 5)^2 - 1\).

Step 2 :Solve for x to find the intersection points. The solutions are \(x = 5.3 - 0.458257569495584i\) and \(x = 5.3 + 0.458257569495584i\).

Step 3 :Substitute the x-values into either of the original equations to find the corresponding y-values. The solutions are \(y = -1.12 - 0.27495454169735i\) and \(y = -1.12 + 0.27495454169735i\).

Step 4 :The solutions to the system of equations are complex numbers, which means that the graphs of the two functions do not intersect at any real points.

Step 5 :\(\boxed{\text{The system of equations has no real solutions.}}\)

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