Algebra-2

To determine which system of equations has the point (1, 0, 5) as a solution, we will substitute x = 1, y = 0, and z = 5 into each system of equations and check if all equations in the system are satisfied.

1. System 1

Equation 1: x + y + z = 6 ⟹ 1 + 0 + 5 = 6 ⟹ 6 = 6 (True)

Equation 2: 2x - y + 3z = 17 ⟹ 2(1) - 0 + 3(5) = 17 ⟹ 2 + 0 + 15 = 17 ⟹ 17 = 17 (True)

Equation 3: -x + y + z = 4 ⟹ -1 + 0 + 5 = 4 ⟹ 4 = 4 (True)

Conclusion for System 1: All equations are satisfied.

 

2. System 2

Equation 1: 2x + 4y + z = 12 ⟹ 2(1) + 4(0) + 5 = 12 ⟹ 2 + 0 + 5 = 12 ⟹ 7 = 12 (False)

Equation 2: x - 2y + z = 4 ⟹ 1 - 2(0) + 5 = 4 ⟹ 1 + 0 + 5 = 4 ⟹ 6 = 4 (False)

Equation 3: -x + 3y + z = 8 ⟹ -1 + 3(0) + 5 = 8 ⟹ -1 + 0 + 5 = 8 ⟹ 4 = 8 (False)

Conclusion for System 2:...