SAT Math: 4x - 6y = 18 and kx + 9y = p Infinitely Many Solutions, Find p/k

Exact Question Text

In the system of equations below, $k$ and $p$ are constants:

> $$ \begin{aligned}

4x - 6y &= 18 \\

kx + 9y &= p

\end{aligned}

$$

If the system has infinitely many solutions, what is the value of $\frac{p}{k}$?

Step-by-Step Algebraic Solution

1. Proportionality: $\frac{4}{k} = \frac{-6}{9} = \frac{18}{p}$
2. Middle ratio: $\frac{-6}{9} = -\frac{2}{3}$
3. $k = -6$, $p = -27$
4. $\frac{p}{k} = \frac{-27}{-6} = \frac{9}{2} = \mathbf{4.5}$