Question 807614
Get both equations into slope-intercept form: y = mx + b

L1: 2x - 6y =2
2x - 2 = 6y
y = (1/3)x - (1/3)

L2: 6x + 3y = 12
3y = -6x + 12
y = (-2)x + 4

Graph L1 (red line) and L2 (green line):

{{{ graph( 200, 200, 0, 3, -2, 2, (1/3)x-(1/3), (-2)x+4 ) }}}

Find point of intersection p1:

Substitute L2 [y = (-2)x + 4] for y in L1 and solve for x:

(-2)x + 4 = (1/3)x - (1/3)
(1/3)x + 2x = 4 + (1/3)
(3/3)x + 6x = 12 + (3/3)
x + 6x = 12 + 1
7x = 13
x = 13/7

Find y:
y = (-2)(13/7) + 4
y = (-26/7) + (28/7)
y = 2/7

p1 = (13/7, 2/7)

The sum of the coordinates is:
13/7 + 2/7
15/7
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