For certain
values of and the system. What are the values of K an M, so that it is an infinite solution.
\(\begin{align*} 3a + 2b &= 2, \\ 6a + 2b &= k - 3a - mb \end{align*}\)
The system of equations has an infinite solution when there are infinitely many pairs of values for a and b that satisfy both equations. To find the values of k and m that satisfy this condition, we can use the following steps:
Solve the first equation for a:
a = (2 - 2b) / 3
Substitute this expression for a into the second equation:
6 * ((2 - 2b) / 3) + 2b = k - 3 * ((2 - 2b) / 3) - mb
4 - 4b + 2b = k - 2 - mb
2 = k - mb
Now we have a single equation with two unknowns, k and m. We can solve this equation for k by letting b = 0. When b = 0, we get k = 2. Therefore, the values of k and m that satisfy the condition for an infinite solution are k = 2 and m = 0.
