Equations of straight lines

Find the equation of the line L passing through the point (8,1) and the
intersection of the lines
L1: 2x+2y-3=0 ------------(1)
L2: 6x-7y-7=0 -----------(2)
(1)*3 - (2),
6x + 6y - 9 - 6x + 7y + 7 = 0
13y = 2
y = 2/13
Sub y = 2/13 into (1)
2x + 2/13 - 3 = 0
2x - 37/13 = 0
2x = 37/13
x = 37/26
Intersection point of L1,L2 = (37/26, 2/13)
Slope of the required equation
= (1 - 2/13)/(8 - 37/26)
= (24/13)/(171/26)
= 48/171
Hence,
the required equation:
(y - 1) = 48(x-8)/171
171y - 171 = 48x - 384
171y = 48x - 213

Let the line be 2x+2y-3+k(6x-7y-7)=0
Sub (8,1) into it, 16+2-3+k(48-7-7)=0
15+34k=0=>k=-15/34
Hence the line is 2x+2y-3-(15/34)(6x-7y-7)=0
68x+68y-102-90x+105y+105=0
173y-22x+3=0