Final answer:
The given system of linear equations has infinitely many solutions or a three-parameter family of solutions.
Step-by-step explanation:
The given system of linear equations is:
x₁ + x₂ + x₃ = 7
x₁ + x₂ + x₃ = 19
By comparing the two equations, we can see that they are the same, which means that these equations are equivalent and represent the same line in a three-dimensional coordinate system.
Therefore, the system of linear equations has infinitely many solutions or a three-parameter family of solutions (A).