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For certain values of $k$ and $m,$ the system
a + 2b = -3 - 7a + b,
4a + 2b = k - 5a - mb
has infinitely many solutions $(a,b).$ What are $k$ and $m?$

 Aug 10, 2024
 #1
avatar+10 
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For a system of equations to have infinitely many solutions, the equations should be the same. We start by simplifying:

\(8a+b=-3\)

\(9a+(2-m)b=k\)

now we make the a terms the same:

\(8a+\frac{8}{9}*(2-m)b=\frac{8k}{9}\)

this means

 \(\frac{8k}{9}=-3, so\: k=-\frac{27}{8}\)

and

\(2-m=1, so\:m=1\)

 Aug 10, 2024

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