If two times x is 5 greater than three times y, what is the value of y

We have \(2x = 3y + 5 \implies 2x - 3y = 5 \implies y = \frac{2}{3}x - \frac{5}{3}\)

Note that the question asked what the value of \(y\) in terms of \(x\), not the specific value of \(y\).

When we have two equation \(y=a_1x+b_1\) and \(y=a_2x+b_2\). These equations have root if and only if \(\frac{a_1}{a_2} \neq \frac{b_1}{b_2}\).

A. \(y=2x-5\). These questions have root, so insufficient.
B. \(y=6x-5\). Same as A, so insufficient.
C. \(y=\frac{x}{2}-5\). Same as A, so insufficient.
D. \(y=\frac{x}{3}-5 \). Same as A, so insufficient.
E. \(y=\frac{2x-5}{3} = \frac{2}{3}x-\frac{5}{3}\). This equation is the same as the given equation, hence two these equations donot have root. Sufficient.

The answer is E.