Using graphical method, find whether following system of linear equations is consistent or not : $x = 0$ and $y = -7$
Generated by claude-sonnet-4-6 · 2026-06-15 10:35 · grounding rag
Model Answer
The equation $x = 0$ represents the y-axis (a vertical line passing through the origin), and $y = -7$ represents a horizontal line parallel to the x-axis, passing through (0, −7).
These two lines intersect at the point (0, −7).
Since the lines intersect at exactly one point, the system has a unique solution. Therefore, the pair of equations is consistent.
Source: Pair of Linear Equations in Two Variables, Section 3.2
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Explanation
- Examiners expect you to identify what each line looks like on the graph (vertical/horizontal), state the point of intersection, and conclude with the word "consistent."
- $x = 0$ is the y-axis; $y = -7$ is a horizontal line — they are perpendicular and always intersect at one point.
- The key rule: intersecting lines → unique solution → consistent. Write this conclusion explicitly or you lose the mark.