+331 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 $m?$
+10 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
\(2-m=1, so\:m=1\)
