C

Step 1: [Equation 1.]- 16x + 17y = 32

Step 2: [Equation 2.]- 64x - y = - 10

Step 3: [Solve Equation 2 for y.]y = - 64x + 10

Step 4: [Substitute the values.]- 16x + 17(- 64x + 10) = 32

Step 5: [Distributive property.]- 16x - 1088x + 170 = 32

Step 6: [Group the like terms.]-1104x + 170 = 32

Step 7: [Subtracting 170 from the two sides of the equation.]-1104x = -138

Step 8: [Solve for x.]x = 18

Step 9: [Substitute the values.]y = - 64(18) + 10

Step 10: [Solve for y.]y = 2

Step 11: So, the ordered pair (18, 2) is the solution for the linear system.

Step 12: The linear system has exactly one solution.