pre-cal help?

Question

1)the sum of two numbers is twice their difference. the larger number is 6 more than twice the smaller. Find the 2 numbers.

Answer 1

The first statement translates into the system:
a+b=2(a-b)
a=2*b+6

which has the solution a=18, b=6

Answer 2

This is just algebra.
Let the two numbers be y and x. You have two equations and two unknowns.

y + x = 2(y - x)
y = 2x + 6

Solve for y in the first equation.

y + x = 2(y - x) = 2y - 2x
3x = y

Plug into the second equation and solve for x.

2x + 6 = 3x
x = 6

y = 3x = 18

The two numbers are 6 and 18.