Algebra-2

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

1. System 1

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

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

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

Conclusion for System 1: Not satisfied.

 

2. System 2

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

Equation 2: 3y + z = 10 ⟹ 3(2) + 4 = 10 ⟹ 6 + 4 = 10 ⟹ 10 = 10 (True)

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

Conclusion ...