Final answer:
The statement is true because the solution set of a linear system is, indeed, a list of values that, when substituted into each equation of the system, turns them into true statements, confirming the validity of the solutions.
Step-by-step explanation:
The statement that "The solution set of a linear system involving variables x₁, ..., xₙ is a list of numbers (s₁, ..., sₙ) that makes each equation in the system a true statement when the values s₁, ..., sₙ are substituted for x₁, ..., xₙ, respectively" is true. To elaborate, when you have a system of linear equations, every equation represents a line in an n-dimensional space, where n is the number of variables.
The solution set refers to the points where all these lines intersect. So, for each equation, when we substitute the solution values for the variables, we turn the equality into a true statement. This process is essential for solving linear systems, which typically involves techniques such as substitution, elimination, or matrix operations.
Let's consider the examples given in the practice test solutions for linear equations. For instance, the equation y = x + 4 is a linear equation where if we know the value of x, we can determine the y value that makes this equation true.
Similarly, in a system involving this equation, the solution for x would be substituted, yielding the corresponding y value that satisfies the equation. This concept also follows the disjunctive syllogism in logic, where the conclusion must be true if the premises (in this case, the equations) are true after replacing the variables with their solutions.