# 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?

Oct 3, 2015

$\left\{\begin{matrix}y = 2 x + 1 \\ 3 x = y + 6\end{matrix}\right.$

#### 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
$\rightarrow y = 2 x + 1$ (in algebraic form)

Three times the smaller exceeds the larger by six
$\rightarrow 3 x = y + 6$ (in algebraic form)

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