Let Davy's present age be D and Christine's be:
We know that:
[tex]D-7=6(C-7) \\ D-7=6C-42 \\ D=6C-35[/tex]
and
[tex]D+1=2(C+1) \\ D+1=2C+2 \\ D=2C+1
[/tex]
So 2C+1 is equal 6C-35
[tex]2C+1=6C-35 \\ 36=4C \\ 9=C[/tex]
Therefore Christine is 9 and Davy is (2*9)+1=19 years old