Using graphical method, solve the following system of equations:
$$3x + y + 4 = 0 \quad \text{and} \quad 3x - y + 2 = 0$$
Generated by claude-sonnet-4-6 · 2026-06-15 10:32 · grounding rag
Model Answer
Equation 1: $3x + y + 4 = 0 \Rightarrow y = -3x - 4$
| $x$ | 0 | –1 | –2 |
|-----|---|----|----|
| $y$ | –4 | –1 | 2 |
Equation 2: $3x - y + 2 = 0 \Rightarrow y = 3x + 2$
| $x$ | 0 | –1 | 1 |
|-----|---|----|---|
| $y$ | 2 | –1 | 5 |
Graph: Plot both lines on the same coordinate axes using the above points.
The two lines intersect at the point $(-1, -1)$.
Verification:
- Eq. 1: $3(-1) + (-1) + 4 = -3 - 1 + 4 = 0$ ✓
- Eq. 2: $3(-1) - (-1) + 2 = -3 + 1 + 2 = 0$ ✓
Solution: $x = -1,\ y = -1$
Since the lines intersect at exactly one point, the pair of equations is consistent with a unique solution.
Source: Chapter 3 (Pair of Linear Equations in Two Variables), Graphical Method
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Explanation
- Table of values: Always make a table with at least 3 points per line — examiners check this step (1 mark each table).
- Graph instruction: Even if you can't draw here, mention "plot and draw both lines" — in the actual exam, draw neatly on graph paper.
- Intersection point: Clearly state the coordinates where lines meet (carries key marks).
- Verification: Always substitute back into both equations — this is expected and fetches 1 mark.
- Conclusion: State "consistent, unique solution" to complete the answer as per CBSE expectations.