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Pair of Linear Equations in Two Variables
RD Sharma
CBSE
Grade 10

Question:

Solve for $x$ and $y$:
$x/2 + 2y/3 = -1$ and $x - y/3 = 3$.

Step-by-Step Solution

Key Concept: Multiply 1st by 6: $3x + 4y = -6$. Multiply 2nd by 3: $3x - y = 9$. Subtract: $5y = -15 \Rightarrow y = -3, x = 2$.
(1) $3x + 4y = -6$, (2) $3x - y = 9$. [0.5 Mark]
Subtract (2) from (1): $5y = -15 \Rightarrow y = -3$. [1.0 Mark]
$3x - (-3) = 9 \Rightarrow 3x = 6 \Rightarrow x = 2$. Solution: $x = 2, y = -3$. [0.5 Mark]

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🎯 Official CBSE Marking Scheme:
Converting fractions to standard form: 0.5 Mark
Solving $y = -3$: 1.0 Mark
Solving $x = 2$: 0.5 Mark

Correct Answer:
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