Solve the system graphically or algebraically.Find the solution(s) accurate to three decimal places. $\left\{ \begin{array} { r }
y - e ^ { - x } = 3 \
y - \ln x = 5
\end{array} \right.$
A)(3.752, 0.287)
B)(0.387, 3.852)
C)(0.287, 3.752)
D)(0.287, 3.852)
E)(3.852, 0.387)

Question

Solve the system graphically or algebraically.Find the solution(s) accurate to three decimal places.  $\left\{ \begin{array} { r } 
y - e ^ { - x } = 3 \
y - \ln x = 5
\end{array} \right.$  
A)(3.752, 0.287)
B)(0.387, 3.852)
C)(0.287, 3.752)
D)(0.287, 3.852)
E)(3.852, 0.387)

Quizplus · Accepted Answer

To solve the system algebraically, we can set the two equations equal to each other since they both equal $y$:$$y = e^{-x} + 3$$$$y = \ln(x) + 5$$Setting them equal to each other gives:$$e^{-x} + 3 = \ln(x) + 5$$Solving this equation requires numerical methods or graphing because it involves both $e^{-x}$ and $\ln(x)$. Graphing these equations or using a numerical solver, we find that the solution is approximately $x = 0.287, y = 3.752$, which corresponds to choice C.

Solve the System Graphically or Algebraically {y−e−x=3y−ln⁡x=5\left\{ \begin{array} { r } y - e ^ { - x } = 3 \\y - \ln x = 5\end{array} \right.{y−e−x=3y−lnx=5​

Solve the System Graphically or Algebraically $\left\{ \begin{array} { r } y - e ^ { - x } = 3 \\y - \ln x = 5\end{array} \right.$