Algebra-2

To determine which system of equations has the point (1, 1, 4) as a solution, we will substitute x = 1, y = 1, and z = 4 into each system of equations and check if the equations are satisfied.

 

1. System 1

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

Equation 2: x - y + z = 2 ⟹ 1 - 1 + 4 = 2 ⟹ 4 = 2 (False)
Equation 3: 2x + 3y - z = 5 ⟹ 2(1) + 3(1) - 4 = 5 ⟹ 2 + 3 - 4 = 5 ⟹ 1 = 5 (False) 

Conclusion for System 1: Not satisfied.

 

2. System 2

Equation 1: 2x - y + z = 3 ⟹ 2(1) - 1 + 4 = 3 ⟹ 2 - 1 + 4 = 3 ⟹ 5 = 3 (False) 
Equation 2: x + 2y + z = 8 ⟹ 1 + 2(1) + 4 = 8 ⟹ 1 + 2 + 4 = 8 ⟹ 7 = 8 (False)
Equation 3: -x + y - z = 2 ⟹ -1 + 1 - 4 = 2 ⟹ -4 = 2 (False)

Conc...