Pair of Linear Equations in Two Variables
RD Sharma
CBSE
Grade 10
Question:
If the equations $x - y = 1$ and $2x + y = 8$ intersect at $(p, q)$, then the values of $p$ and $q$ are:
(a) $p = 3, q = 2$
(b) $p = 2, q = 3$
(c) $p = 4, q = 0$
(d) $p = 5, q = -2$
Step-by-Step Solution
Key Concept: Adding equations: $3x = 9 \Rightarrow x = 3$. Then $3 - y = 1 \Rightarrow y = 2$.
Add: $(x - y) + (2x + y) = 1 + 8 \Rightarrow 3x = 9 \Rightarrow x = p = 3$. [0.5 Mark]
$y = q = 3 - 1 = 2$. Values are $p = 3, q = 2$. [0.5 Mark]
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🎯 Official CBSE Marking Scheme:
Solving for $x = 3$: 0.5 Mark
Solving for $y = 2$: 0.5 Mark
Correct Answer: $p = 3, q = 2$
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