Question

The system of linear equations {

x₁ + x₂ + x₃ = 7
x₁ + x₂ + x₃ = 19 } has
A. a three-parameter family of solutions
B. exactly one solution
C. a two-parameter family of solutions
D. no solution
E. a one-parameter family of solutions

Answer 1

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).