The pair 3x + 2y = 5 and (2a + b)x + (a + 2b)y = 15 has infinitely many solutions…

Step 1. The constants. $\dfrac{5}{15} = \dfrac{1}{3}$, so each coefficient of the first line is $\dfrac{1}{3}$ of the second one's.

Step 2. Two equations. $2a + b = 3 \times 3 = 9$ and $a + 2b = 3 \times 2 = 6$.

Step 3. Solve. From the first, $b = 9 - 2a$. Then $a + 18 - 4a = 6$, so $a = 4$ and $b = 1$.

Step 4. Check. $2a + b = 9$ and $a + 2b = 6$, so the second line is $9x + 6y = 15$, which is $3$ times $3x + 2y = 5$.