Answer: (x,y) = (2,-1)
Work Shown
Solve the first equation for x.
x + 7y = -5
x = -7y-5
Plug this into the other equation to solve for y.
-6x + 7y = -19
-6(-7y-5) + 7y = -19
42y+30+7y = -19
49y = -19-30
49y = -49
y = -49/49
y = -1
Use this y value to determine x.
x = -7y-5
x = -7(-1)-5
x = 7-5
x = 2
The solution is the ordered pair (x,y) = (2,-1)
This is where the two lines intersect.