Answer
Answer A
Work Step by Step
Draw a graph to find the solution of the system.
$2x+3y=-17$
$\rightarrow 3y=-2x-17$
$\rightarrow y=\frac{-2}{3}x-\frac{17}{3}$
The slope is $\frac{-2}{3}$. The y-intercept is $\frac{17}{3}$.
$3x+2y=-8$
$\rightarrow 2y=-3x-8$
$ \rightarrow y=-\frac{3}{2}x-4$
The slope is $-\frac{1}{4}$. The y-intercept is $\frac{5}{4}$.
Find the point of intersection. The lines appear to intersect at $(2,-7)$. Check to see if $(2,-7)$ makes both equations true.
$y=\frac{-2}{3}x-\frac{17}{3} \rightarrow -7=\frac{-2}{3}(2)-\frac{17}{3} \rightarrow -7=-7$
$y=-\frac{3}{2}x-4 \rightarrow -7=-\frac{3}{2}(2)-4 \rightarrow -7=-7$
The solution of the system is $(2,-7)$.
Answer A is correct.
