tentukan himpunan penyelesaian dari sistem persamaan{-3a-b-3c=-8 -5a+3b+6c=-4 6a-4b+c=-20!

Jawaban: a = 41/16 b = 131/16 c = -21/8 Penjelasan: -3a - b - 3c = -8 ... (1) -5a + 3b + 6c = -4 ... (2) 6a - 4b + c = -20 ... (3) Eliminasi (1) dan (2) -3a - b - 3c = -8 |x 3 -5a + 3b + 6c = -4 -9a - 3b - 9c = - 24 -5a + 3b + 6c = -4 ------------------------ + -14a - 3c = -28 ... (4) Eliminasi (1) dan (3) -3a - b - 3c = -8 |x 4 6a - 4b + c = -20 -12a - 4b - 12c = -32 6a - 4b + c = -20 --------------------------- - -18a - 13c = -12 ... (5) Eliminasi (4) dan (5) -14a - 3c = -28 |x 13 -18a - 13c = -12 |x 3 -182a - 39c = -364 -54a - 39c = -36 ------------------------- - -128a = -328 a = 41/16 Substitusi ke persamaan (4) -14(41/16) - 3c = -28 -287/8 - 3c = -28 - 3c = -28 + 287/8 - 3c = 63/8 c = -63/24 c = -21/8 Substitusi ke persamaan (1) -3(41/16) - b - 3(-63/24) = -8 -123/16 - b + 189/24 = -8 - b = -8 + 123/16 - 189/24 - b = (-384 + 369 - 378)/48 b = 393/48 b = 131/16 diperoleh a = 41/16 b = 131/16 c = -21/8