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

Question:

Solve the pair of linear equations by elimination method:
$3x + 4y = 10$ and $2x - 2y = 2$.

Step-by-Step Solution

Key Concept: Multiply 2nd equation by $2$: $4x - 4y = 4$. Add to 1st equation: $7x = 14 \Rightarrow x = 2$. Then $y = 1$.
Multiply 2nd equation by $2$: $4x - 4y = 4$. [0.5 Mark]
Add to 1st equation: $(3x + 4y) + (4x - 4y) = 10 + 4 \Rightarrow 7x = 14 \Rightarrow x = 2$. [1.0 Mark]
Substitute $x = 2$ in $2(2) - 2y = 2 \Rightarrow 2y = 2 \Rightarrow y = 1$. Solution: $x = 2, y = 1$. [0.5 Mark]

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🎯 Official CBSE Marking Scheme:
Multiplying equation: 0.5 Mark
Solving $x = 2$: 1.0 Mark
Solving $y = 1$: 0.5 Mark

Correct Answer:
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