Chapter 10 - Systems of Equations and Inequalities - Section 10.6 Systems of Nonlinear Equations - 10.6 Assess Your Understanding - Page 795: 77

$5$

1. Use the given conditions, we can set up the following: $\begin{cases}\frac{a}{b}=\frac{2}{3} \\ a+b=10 \end{cases}$ 2. From the 1st equation, we can get $a=(\frac{2}{3})b$ 3. Plug it in the 2nd equation to get $(\frac{2}{3})b+b=10$ or $(\frac{5}{3})b=10$, thus $b=6$, 4. Use the 2nd equation again to get $a=4$ 5. We can get: $\frac{a+b}{b-a}=\frac{10}{2}=5$