Solve the system graphically.
-$$\begin{array} { l }
y = \ln ( 3 x - 2 ) \
x ^ { 2 } + 3 y ^ { 2 } = 7
\end{array}$$
A) $\approx ( 5.25,2.62 )$
B) $\approx ( 0.74 , - 1.47 )$ and $\approx ( 1.73,1.16 )$
C) $\approx ( 1.73 , - 1.16 )$ and $\approx ( 0.74,1.47 )$
D) $\approx ( 0.77,1.46 )$ and $\approx ( - 0.59 , - 1.49 )$

Question

Solve the system graphically.
-$$\begin{array} { l } 
y = \ln ( 3 x - 2 ) \
x ^ { 2 } + 3 y ^ { 2 } = 7
\end{array}$$
A) $\approx ( 5.25,2.62 )$
B) $\approx ( 0.74 , - 1.47 )$ and $\approx ( 1.73,1.16 )$
C) $\approx ( 1.73 , - 1.16 )$ and $\approx ( 0.74,1.47 )$
D) $\approx ( 0.77,1.46 )$ and $\approx ( - 0.59 , - 1.49 )$

Quizplus · Accepted Answer

The system of equations involves a logarithmic function and an ellipse. Graphically solving, we look for intersections between the curve $y = \ln(3x - 2)$ and the ellipse defined by $x^2 + 3y^2 = 7$. The correct intersections are approximately at $(0.74, -1.47)$ and $(1.73, 1.16)$, which correspond to choice B.

Solve the System Graphically y=ln⁡(3x−2)x2+3y2=7\begin{array} { l } y = \ln ( 3 x - 2 ) \\x ^ { 2 } + 3 y ^ { 2 } = 7\end{array}y=ln(3x−2)x2+3y2=7​

Solve the System Graphically $\begin{array} { l } y = \ln ( 3 x - 2 ) \\x ^ { 2 } + 3 y ^ { 2 } = 7\end{array}$