Use a graphing calculator to approximate the solutions of the system. $$\left\{ \begin{array} { c }
3.8 x + 3.9 y = 38.03 \
- 9 x + 4 y = 14.5
\end{array} \right.$$
A) $\quad ( 7.9,1.9 )$
B) $\quad ( - 6,10.8 )$
C) $\quad ( - 1.9 , - 7.9 )$
D) $\quad ( 1.9,7.9 )$
E) $\quad ( 9.8 , - 5 )$

Question

Use a graphing calculator to approximate the solutions of the system. $$\left\{ \begin{array} { c } 
3.8 x + 3.9 y = 38.03 \
- 9 x + 4 y = 14.5
\end{array} \right.$$
A) $\quad ( 7.9,1.9 )$
B) $\quad ( - 6,10.8 )$
C) $\quad ( - 1.9 , - 7.9 )$
D) $\quad ( 1.9,7.9 )$
E) $\quad ( 9.8 , - 5 )$

Quizplus · Accepted Answer

To use a graphing calculator, we need to first convert the system into slope-intercept form, $y=mx+b$. We can do this by solving for $y$ in each equation:
\begin{align*}
3.8x+3.9y&=38.03\
3.9y&=-3.8x+38.03\
y&=-\frac{3.8}{3.9}x+9.74
\end{align*}
and
\begin{align*}
-9x+4y&=14.5\
4y&=9x+14.5\
y&=\frac{9}{4}x+\frac{29}{8}
\end{align*}
We can now graph both equations on the calculator using the $y=$ function. We can then find the point of intersection of the two lines by using the 2nd function and the Trace function to move the cursor to the point of intersection. From the graph, we can see that the point of intersection is approximately $(1.9,7.9)$. Therefore, the best choice is D.

Use a Graphing Calculator to Approximate the Solutions of the System