The line kx + my = 26 passes through the point (3, 4) and the equation kx + 4my = 22 (using the same k and m) is satisfied by x=1, y=1.…

The first line passes through $(3, 4)$, so $3k + 4m = 26$. The second equation holds at $(1, 1)$, so $k + 4m = 22$. Subtract the second from the first: $2k = 4$, so $k = 2$. Then $2 + 4m = 22$ gives $m = 5$. So $k + m = 7$, choice A. Check the first equation: $6 + 20 = 26$. Choices B (10), C (6), and D (16) do not match $k = 2$ and $m = 5$; each comes from an arithmetic slip in subtracting the equations, or from combining the right sides, such as $26 - 10$. Name both unknowns and eliminate one by subtraction.