determine the coordinates of the vertices of the triangle, and then find the exact coordinates of the centroid

Question

determine the coordinates of the vertices of the triagngle formed by the lines: (algebraic solution)
2x + 5y = 16
4x - 3y = 6
3x + y = -2

Find the EXACT coordinates fo the centroid
(you solution should be algebraic)

Answer 1

solving the systems you get
A(0,-2)
B(-2,4) and
C(3,2)
centroid
Xc= (0-2+3)/3 =1/3
Yc=(-2+4+2)/3=4/3