X+2y=1
X-y=-5

Assuming you are looking for "Point" of intersection:

Choose one, solve for "x"

add y to both sides of equality:
X-y=-5
 +y +y
X=y-5

Now replace "y-5" for "X" in the other equation:
X+2y     = 1
(y-5)+2y = 1
y-5+2y   = 1

Combine "y" (Add)
3y -5     = 1

Add 5 to both sides of equality:
3y -5     = 1
   +5      +5

Divide both sides by 3 to solve for y:
3y        = 6
(3y)/3    = (6)/3
y         = 2

We have found "y" but this is not a 2D point. We need an "X".

Choose one of the top two equations:
X-y=-5

Substitute "2" for "y" because we found "y=2":
x-2=-5

Add "2" to both sized of equalty:
x-2=-5
 +2 +2
x  = -3

We have found "x"

Now, answer in "Point Format"
P(x,y)=P(-3,2)

These two equations for lines (X+2y=1) and (X-y=-5) intersect at point P(x,y)=P(-3,2)

HTH