Final answer:
To describe the solution set as a line in ℝ³, we can use the vectors (5, -2, 0) and (1, -7, 1) which represent the coefficients of x₃ in the given equations. The general form of a point on the line is (5, -2, 0) + t(1, -7, 1), where t is a scalar. Therefore, the solution set of the system of linear equations can be described as a line in ℝ³.
Step-by-step explanation:
To describe the solution set as a line in ℝ³, we can use the vectors (5, -2, 0) and (1, -7, 1) which represent the coefficients of x₃ in the given equations. We can express any point on the line as a linear combination of these two vectors.
The general form of a point on the line is (5, -2, 0) + t(1, -7, 1), where t is a scalar. This equation represents a parametric form of the line, with (5, -2, 0) as the initial point and (1, -7, 1) as the direction vector.
Therefore, the solution set of the system of linear equations can be described as a line in ℝ³.