Q1. [3] § 3.3 Algebraic Methods of Solving a Pair of Linear Equations § 3.3.1 Substitution Method § 3.3.2 Elimination Method
If $217x + 131y = 913$ and $131x + 217y = 827$, then solve the equations for the values of $x$ and $y$.
Previously asked in CBSE board exam
2023 30/2/1 Q30(b) (OR-2)
Generated by claude-sonnet-4-6 · 2026-06-15 10:33 · grounding rag
Model Answer
Given:
$$217x + 131y = 913 \tag{1}$$
$$131x + 217y = 827 \tag{2}$$
Adding (1) and (2):
$$348x + 348y = 1740$$
$$x + y = 5 \tag{3}$$
Subtracting (2) from (1):
$$86x - 86y = 86$$
$$x - y = 1 \tag{4}$$
Adding (3) and (4):
$$2x = 6 \implies x = 3$$
Substituting in (3):
$$3 + y = 5 \implies y = 2$$
∴ x = 3, y = 2
Source: Chapter 3, Section 3.3.2 (Elimination Method)
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Explanation
- The trick here is to add and subtract the two equations directly — this instantly simplifies the large coefficients (217 and 131) into manageable ones (348 and 86), avoiding tedious multiplication.
- Examiners award marks for: setting up the addition/subtraction step clearly, getting both simplified equations, solving for x and y, and stating the final answer.
- Always verify: 217(3) + 131(2) = 651 + 262 = 913 ✓ and 131(3) + 217(2) = 393 + 434 = 827 ✓
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