Algebra-2

To find out which system of equations has the point (2, 3, 1) as a solution, we will substitute x = 2, y = 3, and z = 1 into each system of equations and check if all equations in the system are satisfied.

1. System 1

Equation 1: x + y + z = 6 ⟹ 2 + 3 + 1 = 6 ⟹ 6 = 6 (True)

Equation 2: 2x - 3y + z = -4 ⟹ 2(2) - 3(3) + 1 = -4 ⟹ 4 - 9 + 1 = -4 ⟹ -4 = -4 (True)

Equation 3: 3x + y - z = 8 ⟹ 3(2) + 3 - 1 = 8 ⟹ 6 + 3 - 1 = 8 ⟹ 8 = 8 (True)

Conclusion for System 1: All satisfied.

 

2. System 2

Equation 1: 2x + y - z = 5 ⟹ 2(2) + 3 - 1 = 5 ⟹ 4 + 3 - 1 = 5 ⟹ 6 = 5 (False)

Equation 2: -x + 2y + 3z = 10 ⟹ -2 + 2(3) + 3(1) = 10 ⟹ -2 + 6 + 3 = 10 ⟹ 7 = 10 (False)

Equation 3: 3x - y + z = 4 ⟹ 3(2) - 3 + 1 = 4 ⟹ 6 - 3 + 1 = 4 ⟹ 4 = 4 (True)