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Pair of Linear Equations in Two Variables
NCERT Exemplar
CBSE
Grade 10
Question:
If $x = a$ and $y = b$ is the solution of the equations $x - y = 2$ and $x + y = 4$, then the values of $a$ and $b$ are respectively: (a) $3, 5$ (b) $5, 3$ (c) $3, 1$ (d) $-1, -3$
Step-by-Step Solution
Key Concept: Solve the system by elimination: add the two equations.
Adding $x - y = 2$ and $x + y = 4$: $2x = 6 \Rightarrow x = 3$, so $a = 3$. [0.5 Mark] Substituting $x = 3$ into $x + y = 4$: $3 + y = 4 \Rightarrow y = 1$, so $b = 1$. [0.5 Mark]
--- 🎯 Official CBSE Marking Scheme: Solving for $x=a=3$: 0.5 Mark Solving for $y=b=1$: 0.5 Mark
Correct Answer:$3, 1$
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