I need help doing these problems

I have the answers but need to know how to do them

Find the point of intersection for each of the following pair of lines
y=4x-1 and y=5+2x I have (3,11) but how do you work this

another is
x+y=6 and x-y=2 and i have (4,2) how did I get this?

These are essentially problems in simultaneous equations, so use simultaneous equation methods.

y=4x-1 and y=5+2x
Set the two expressions for y equal to each other:
4x-1 = 5+2x
Combine like terms:
2x = 6
x = 3
Substitute this value for x into either of the given equations and evaluate y:
y = 4(3) - 1 = 11

x+y=6 and x-y=2
Add the two equations:
2x = 8
x = 4
Substitute this value for x into either of the given equations and solve for y:
4 + y = 6
y = 2