If:
x + y = 1000
then:
y = 1000 - x
We can plug that into the other equation to solve for a value of x.
0.06x = 0.04y
0.06x = 0.04(1000-x)
0.06x = 40-0.04x
0.1x = 40
x = 400
We can then solve for y:
y = 1000 - 400
y = 600
Therefore, x = 400 and y = 600.