Find the equation of the line that passes through the point of intersection of 3x-y=10 and 4x+2y=10, and that is perpendicular to 2x-6y+24=0

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