Deriving d = v2Δt - 1/2aΔt^2

To derive the equation d = v2Δt - 1/2aΔt^2 you must first substitute v1 into Equation 2.

Equation #2:
d = 1/2(v1+v2)Δt

It can easily done by doing this:
d = 1/2(v2+v1)Δt

d = 1/2(v2+v2=aΔt)Δt

Which would therefore create:

d = v2Δt = 1/2aΔt^2

You can also use an almost similar method to derive d =v1Δt+1/2aΔt^2

Substitute the expression for v2 into Equation #2:

d = 1/2(v2+v1)Δt

d = 1/2(v1+aΔt+v1)Δt

Which would therefore get:
d = v1Δt+1/2aΔt^2