Algebra-2

To determine which system of equations has the point (4, 0, 2) as a solution, we will substitute x = 4, y = 0, and z = 2 into each system of equations and check if the equations are satisfied.

1. System 1

Equation 1: x + y + z = 6 ⟹ 4 + 0 + 2 = 6 ⟹ 6 = 6 (True)

Equation 2: 2x + 3y - z = 10 ⟹ 2(4) + 3(0) - 2 = 10 ⟹ 8 + 0 - 2 = 10 ⟹ 6 = 10 (False)
Equation 3: x - 2y + z = 2 ⟹ 4 - 2(0) + 2 = 2 ⟹ 4 + 2 = 2 ⟹ 6 = 2 (False)

Conclusion for System 1: Not satisfied.

 

2. System 2

Equation 1: 3x - 2y + z = 10 ⟹ 3(4) - 2(0) + 2 = 10 ⟹ 12 - 0 + 2 = 10 ⟹ 14 = 10 (False)
Equation 2: x + y - z = 4 ⟹ 4 + 0 - 2 = 4 ⟹ 2 = 4 (False)
Equation 3: 2x + 4y - 3z = 0 ⟹ 2(4) + 4(0) - 3(2) = 0 ⟹ 8 + 0 - 6 = 0 ⟹ 2 = 0 (False)

Conclusion for System 2: Not satisfied.