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

Adding both equations:

$(101x + 102y) + (102x + 101y) = 304 + 305$

$203x + 203y = 609$

$x + y = 3$ … (1)

Subtracting equation 1 from equation 2:

$(102x + 101y) - (101x + 102y) = 305 - 304$

$x - y = 1$ … (2)

Adding (1) and (2): $2x = 4 \Rightarrow x = 2$

Substituting in (1): $2 + y = 3 \Rightarrow y = 1$

∴ x = 2, y = 1

Source: Chapter 3, Section 3.3.2 (Elimination Method)

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• The key trick here is to add and subtract the two equations directly — this instantly eliminates one variable each time, saving steps.
• Examiners expect you to show each algebraic step clearly: the addition/subtraction, the simplified equation, and the substitution back.
• Always write the final answer clearly as "x = …, y = …" for full marks.