Q. The pair of linear equations \(y=0\) and \(y=-7\) has.

Solution (step‑by‑step)

1. Write down the two equations.

   We are given the pair of linear equations
   \(y = 0\) and \(y = -7\).

   • What to do: Record each equation exactly as given.
2. Interpret each equation geometrically.

   The equation \(y = 0\) represents a horizontal line consisting of all points whose y‑coordinate is 0 (the x‑axis). The equation \(y = -7\) represents a horizontal line consisting of all points whose y‑coordinate is \(-7\).

   • What to do: Recognize that equations of the form \(y = c\) are horizontal lines with slope 0 and vertical position given by \(c\).
3. Compare their slopes and intercepts.

   Both lines have slope 0 (they are horizontal). Their y‑intercepts are different: the first has intercept 0, the second has intercept \(-7\).

   • What to do: Check whether slopes are equal or different and whether the constant terms (intercepts) are equal or different.
4. Decide about intersections.

   Two distinct horizontal lines (same slope, different intercepts) are parallel and do not meet. Algebraically, trying to satisfy both equations at once leads to the contradiction
   \(0 = -7\), which is impossible.

   • What to do: Substitute one equation into the other or compare directly to see if there is any common solution; here substitution gives \(0 = -7\), so there is no solution.
5. Conclusion: nature of the pair and solution set.

   The two lines are distinct and parallel, so the system has no solution. In set notation the solution set is the empty set: \(\varnothing\).

   • What to do: State the final classification and the solution set.