Pair of Linear Equations in Two Variables
NCERT Exemplar Ch 03
CBSE_NCERT_EXEMPLAR_CH03
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:
$3, 5$
$5, 3$
$3, 1$
$-1, -3$
Step-by-Step Solution
Key Concept: Solve the system by elimination: add the two equations.
Stepwise Solution:
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]
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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