+673 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 $m?$
+1804 Let's simplify the two equations a bit first. We get that
\(8a + b = -3 \\ 9a + (2 +m)b = k \)
Now,
This will have infinte solutions when the equations are the same...so....multiply the first equation by 9 and the second by 8 and we get
\(72a + 9b = -27 \\\ 72a + 8 (2 + m)b = 8k\)
Thus, we can no easily solve for m and k. Solving for m, we get
\(9 = 8(2 + m) \\ 9 = 16 + 8m \\ -7 = 8m \\ m = -7/8\)
Solving for k, we get
\(8 k = -27 \\ k = -27/8 \)
Thanks! :)
