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Determine $a+b$ such that the following system of equations:

$2x-(a-4)y=2b+1 \text{ and }4x-(a-1)y=5b-1$ infinite solutions.

  1. $11$
  2. $9$
  3. $10$
  4. $8$
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Answer is C

infinitely many solns, so $\frac{a_{1}}{a_{2}}=\frac{b_{1}}{b_{2}}=\frac{c_{1}}{c_{2}}$

$\frac{2}{4}=\frac{-(a-4)}{-(a-1)}=\frac{2b+1}{5b-1}$

On solving, we get a = 7 and b = 3

So, (a+b) = 7 + 3 = 10

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