the equation of two sides of a parallelogram are $2x-3y+7=0$ and $4x+y-21=0$ and one vertex is $(-1,-3)$. Find the other vertices. First, I checked if the point $(-1,-3)$ is not a solution to the two given equations above so therefore none of those lines passes that point. Then, I solved for the lines parallel to equations above getting $2x-3y-7=0$ and $4x+y+7=0$ respectively.
Edit: i managed to find the other vertices which are (5,1), (4,5), and (-2,1). I just want to ask if my vertices are correct.

The parallelogram has $4$ vertices. The vertex $(-1,-3)$ is not an element of both given equations. The $2$ equations given are not parallel to eachother.
This tells us that the equations are from 2 abutting sides. These equations can only obtain $3$ vertices, so the given vertex is the $4^{th}$ vertex. You've already solved it almost. You calculated the equations of the other $2$ sides.
By calculating the $3$ remaining intersection points of the non-parallel equations you've found your other vertices. 
