Question

The larger of two numbers exceeds twice the smaller by one. Three times the smaller exceeds the larger by six. If y is the larger number, what systems of equations represents the word problem?

Answer 1

`{(y=2x+1),(3x=y+6):}`

Explanation:

Assuming `x` can be used to represent the smaller
(we are told `y` represents the larger).

The larger...exceeds twice the smaller by one
`rarr y = 2x+1` (in algebraic form)

Three times the smaller exceeds the larger by six
`rarr 3x = y+6` (in algebraic form)

[It wasn't requested, but using substitution we can fairly easily determine `(x,y) = (7,15)`]