Answer
$(3,4)$
Work Step by Step
To solve this system of equations, we use the graphing method.
$3x+2y=17$
$x=3$
Taking the first equation, we solve for $y$.
$3x+2y=17$
$2y=17-3x$
$y=\frac{17-3x}{2}$
Find three solutions:
For $x=2$,
$y=\frac{17-3(2)}{2}$
$y=\frac{17-6}{2}$
$y=\frac{11}{2}$
$y=5.5$
For $x=0$,
$y=\frac{17-3(0)}{2}$
$y=\frac{17}{2}$
$y=8.5$
For $x=-2$,
$y=\frac{17-3(-2)}{2}$
$y=\frac{17+6}{2}$
$y=-\frac{23}{2}$
$y=11.5$
With the three points, $(2,5.5), (0,8.5), (-2,11.5)$, we can graph the straight line that goes through these points.
Taking the second equation, we see we have no $y$. So this is a vertical line that intersects the point $x=3$.
The intersection point between these two lines is the answer to the system of equations.
