Simultaneous equation question

Tom decides to sell flowers and vegetables from his gate so he makes two rectangular gardens.
The flower garden in 3m longer than it is wide. The length of the vegetable garden is 4m more than double its width. The combined perimeters of the two gardens is 126m.
Tom decides to fence both gardens to keep out his pets. The fencing for the flower garden costs $4 per metre and the fencing for the vegetable garden costs $5 per metre. The total fencing cost for the two gardens is $584.
Find the dimensions of each garden.

Can anyone explain what to do to solve it? My answer book only states the answers but not how to do it.

Thanks!!! :)

If the width of the flower garden is x (in metres), then its length is x + 3, so, since its perimeter is twice the sum of its width and length, its perimeter is 2(x + x + 3) = 4x + 6, and its cost is 4(4x + 6) = 16x + 24 (in dollars.)

If the width of the vegetable garden is y (in metres), then its length is 2y + 4, so its perimeter is 2(y + 2y + 4) = 6y + 8, and its cost is 5(6y + 8) = 30y + 40.

Therefore, we have the equations

4x + 6 + 6y + 8 = 126 (total perimeter)

and

16x + 24 + 30y + 40 = 584 (total cost.)

These simplify to

4x + 6y = 112, 16x + 30y = 520

and subtracting 4 times the first equation from the second gives

6y = 72,

so y = 12. Back-substituting this into the first equation gives 4x = 40, so x = 10. Therefore, the flower garden is 10 by 13 metres and the vegetable garden is 12 by 28 metres.