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IMAS 2011 Junior Division — Second Round Question 12

IMAS · IMAS 2011 Junior Division — Second Round

Question 12

The integers $a_1,a_2,b_1,b_2,c_1,c_2$ and $M$ satisfy
$$(a_1x+b_1y+c_1)(a_2x+b_2y+c_2)=2x^2+10xy+My^2+7x+18y+6$$
for any numbers $x$ and $y$. What is the value of $M$?