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 ---> divide by 2 ---> 3x - 2y = a/2
6y - 9x = b ---> -9x + 6y = b ---> divide by -3 ---> 3x - 2y = b/-3
Since you have 3x - 2y = a/2 and 3x - 2y = b/-3, a/2 = b/-3
---> multiply both sides by 2/b ---> a/b = 2/-3 or -2/3
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