Start with
[tex]\dfrac{2a+3b}{a+b}=7[/tex]
Assuming [tex]a\neq -b[/tex], multiply both sides by [tex]a+b[/tex]
[tex]2a+3b = 7a+7b[/tex]
Solve for [tex]a[/tex]
[tex]5a = -4b \iff a = -\dfrac{4b}{5}[/tex]
Substitute this value for [tex]a[/tex] in the desired expression:
[tex]\dfrac{2a}{b} = \dfrac{\frac{-8b}{5}}{b} = -\dfrac{8}{5}[/tex]
You were correct! :)
