Pair of Linear Equations in Two Variables
RD Sharma
CBSE
Grade 10
Question:
If $2x + y = 23$ and $4x - y = 19$, the value of $5y - 2x$ is:
(a) $31$
(b) $37$
(c) $29$
(d) $33$
Step-by-Step Solution
Key Concept: Add equations: $6x = 42 \Rightarrow x = 7$. $y = 23 - 14 = 9$. $5y - 2x = 5(9) - 2(7) = 45 - 14 = 31$.
Add: $6x = 42 \Rightarrow x = 7, y = 9$. [0.5 Mark]
$5(9) - 2(7) = 45 - 14 = 31$. [0.5 Mark]
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🎯 Official CBSE Marking Scheme:
Solving $x = 7, y = 9$: 0.5 Mark
Evaluating $5y - 2x = 31$: 0.5 Mark
Correct Answer: $31$
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