Let b be Jack's age now, g be Jill's age now.

b = 2g (Jack is twice as old as Jill)

(b+2) = 4(g-9) (in 2 years, Jack will be twice Jill's age 9 years ago)

((2g)+2) = 4g -36 (substitute for b, use the distributive property on the right side)

2g + 38 = 4g (add 36 to both sides)

38 = 2g (subtract 2g from both sides. Recognize this tells us the value of b.

19 = g (divide both sides by 2)

Jack is 38, Jill is 19.

Check

In two years, Jack will be 40, which is 4 times Jill's age 9 years ago, when she was 10.

b = 2g (Jack is twice as old as Jill)

(b+2) = 4(g-9) (in 2 years, Jack will be twice Jill's age 9 years ago)

((2g)+2) = 4g -36 (substitute for b, use the distributive property on the right side)

2g + 38 = 4g (add 36 to both sides)

38 = 2g (subtract 2g from both sides. Recognize this tells us the value of b.

19 = g (divide both sides by 2)

Jack is 38, Jill is 19.

Check

In two years, Jack will be 40, which is 4 times Jill's age 9 years ago, when she was 10.