7M + 9N = 84 (1)
M + N = 7 |•7 => 7M + 7N = 49 (2)
(1) - (2): (7M + 9N) - (7M + 7N) = 84 - 49
7M + 9N - 7M - 7N = 35
2N = 35 |:2
N = 35/2
M + N = 7 => M + 35/2 = 7
M = 7 - 35/2
M = -21/2