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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.

 Mar 30, 2020
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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

 Mar 30, 2020

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