Solve the following pair of linear equations by the elimination method:
$3x + 4y = 10$
$2x - 2y = 2$
Step-by-Step Solution
Key Concept: Multiply second equation by $2$ so the coefficients of $y$ become $+4$ and $-4$, then add.
Multiply second equation by $2$: $4x - 4y = 4$. [0.5 Mark]
Add to first equation: $(3x + 4y) + (4x - 4y) = 10 + 4 \Rightarrow 7x = 14 \Rightarrow x = 2$. [1.0 Mark]
Substitute $x = 2$ into $2(2) - 2y = 2 \Rightarrow 4 - 2y = 2 \Rightarrow 2y = 2 \Rightarrow y = 1$. Solution: $x = 2, y = 1$. [0.5 Mark]
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🎯 Official CBSE Marking Scheme:
Multiplying second equation to match coefficients: 0.5 Mark
Adding equations to eliminate $y$ and finding $x = 2$: 1.0 Mark
Finding $y = 1$: 0.5 Mark
Correct Answer: