y = 4x + 1,   (1)
y =  x + 4.   (2)

Since left sides of these equations are identical (y's), their right sides are equal.

So you have a single equation for x to solve:

4x + 1 = x + 4.    (notice: this is the same as to make a substitution for y).

3x = 3,

x = 1.

Then y = 5.