Solve the following system of equations graphically : $2x - y - 2 = 0$, $-4x + y + 4 = 0$. Also, find the absolute difference between the ordinates of the points where given lines cut y – axis.
Generated by claude-sonnet-4-6 · 2026-06-15 10:34 · grounding rag
Model Answer
Finding points for Line 1: $2x - y - 2 = 0 \Rightarrow y = 2x - 2$
| x | 0 | 1 |
|---|---|---|
| y | –2 | 0 |
Points: (0, –2), (1, 0)
Finding points for Line 2: $-4x + y + 4 = 0 \Rightarrow y = 4x - 4$
| x | 0 | 1 |
|---|---|---|
| y | –4 | 0 |
Points: (0, –4), (1, 0)
Plot both lines on the graph. The two lines intersect at (1, 0).
∴ Solution: x = 1, y = 0
Y-axis intercepts:
- Line 1 cuts y-axis at (0, –2) → ordinate = –2
- Line 2 cuts y-axis at (0, –4) → ordinate = –4
Absolute difference = |–2 – (–4)| = |2| = 2
Source: Chapter 3, Section 3.2
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Explanation
- Table of values earns the first mark; always find two points per line and show them in a table.
- Intersection point (the solution) earns the second mark — read coordinates carefully from the graph.
- The absolute difference of ordinates (y-values where lines meet the y-axis) is the third mark — set x = 0 in each equation to get the y-intercepts quickly.
- "Absolute difference" means take the positive value: $|-2-(-4)| = 2$.