Hello,
1) we must find the point of intersection of the 2 lines
3x-y=10
4x+2y=10
==>10x=30 ==>x=3 and y=3*3-10=-1
(3,-1)
2) we must find the slope of the line:
2x-6y+24=0==>y=x/3+4 slope=1/3
The perpendicular has as slope m*1/3=-1==>m=-3
The equation of the line is y+1=-3(x-3) or y=-3x+8
