-3x + y + z = 2
y = 3x - z + 2
.
5x + 2y - 4z = 21
5x +2(3x - z + 2) - 4z = 21
5x + 6x - 2z + 4 - 4z = 21
11x - 6z + 4 = 21
11x - 6z = 17
-6z = -11x + 17
.
x - 3y - 7z = -10
x - 3(3x - z + 2) - 7z = -10
x - 9x + z - 6 - 7z = -10
-8x - 6z - 6 = -10
-8x - 6z = -4
-8x - 11x + 17 = -4
-19x + 17 = -4
-19x = -21
x = 21 / 19
-6z = -11x + 17
-6z = -11(21 / 19) + 17
-6z = -231 / 19 + 17
-6z = -231 / 19 + 323 / 19
-6z = 92 / 19
z = -92 / 114
z = -46 / 57
y = 3x - z + 2
y = 3(21/19) - -46/57 + 2
y = 63 / 19 + 46 / 57 + 2
y = 189 / 57 + 46 / 57 + 114 / 57
y = (189 + 46 + 114) / 57
y = 349 / 57
Answer: x = 21 / 19, y = 349 / 57, z = -46 / 57