The lines representing the given pair of linear equations are non-intersecting. Which of thefollowing statements is true?

When two linear equations represent non-intersecting lines, it indicates that the lines are parallel. This occurs when the two equations have the same slope but different y-intercepts.

Analysis:

1. Definition of Parallel Lines: The lines represented by the equations have the same slope $m$ and different y-intercepts $c_1$ and $c_2$ such that $c_1 \neq c_2$.
2. Equations of Lines: If you have two linear equations, they can be written in the form: $y = m_1 x + c_1 \quad \text{and} \quad y = m_2 x + c_2$ For the lines to be non-intersecting, it must hold that $m_1 = m_2$ and $c_1 \neq c_2$.
3. Conclusion: Thus, the true statement concerning the non-intersecting nature of the lines would affirm their parallelism.

Final Answer:

The true statement is: The lines are parallel.