Mathematics — Standard (041) — CBSE Class 10 board question

Adding the two equations:

$$2x + y = 13$$
$$4x - y = 17$$

Adding: $6x = 30 \Rightarrow x = 5$

Substituting in $2x + y = 13$: $10 + y = 13 \Rightarrow y = 3$

Therefore, $x - y = 5 - 3 = \mathbf{2}$

Source: Chapter 3, Section 3.3.2 (Elimination Method)

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• Add the two equations to eliminate $y$ (since $+y$ and $-y$ cancel directly) — this is the elimination method.
• Find $x$ first, then substitute back to find $y$.
• The question asks for $(x - y)$, not individual values, so make sure to compute and state the final answer clearly.
• Examiners award 1 mark for correct $x$ and $y$, and 1 mark for the correct value of $(x - y)$.