To solve this system of equations using the substitution method, we can substitute Y = 4x from the first equation into the second equation for Y. This will give us an equation in terms of x only.
X + Y = 5
X + 4x = 5 (substituting Y = 4x)
5x = 5
x = 1
Now that we have solved for x, we can substitute it back into either equation to find the value of Y. Let's use the first equation:
Y = 4x
Y = 4(1)
Y = 4
Therefore, the solution to the system of equations is x = 1 and y = 4.