If the system of equations \begin{align*} 6x-4y&=a,\\ 6y-9x &=b. \end{align*}has a solution $(x, y)$ where $x$ and $y$ are both nonzero, find $\frac{a}{b},$ assuming $b$ is nonzero.
6x - 4y = a → 6x - 4y = a → 6x - 4y = a
6y - 9x = b → -9x + 6y = b → 6x - 4y = (-2/3)b
The determinant of the coefficient matrix = 0
If a = (-2/3)b, we have infinite solutions where x, y are both non-zero
So... we have infinite solutions when a/b = -2/3
