Pair of Linear Equations in Two Variables
RD Sharma
CBSE
Grade 10
Question:
If $2x + 3y = 11$ and $2x - 4y = -24$, then the value of $m$ for which $y = mx + 3$ is:
(a) $-1$
(b) $1$
(c) $2$
(d) $-2$
Step-by-Step Solution
Key Concept: Subtracting equations: $7y = 35 \Rightarrow y = 5$. Then $2x = 11 - 15 = -4 \Rightarrow x = -2$. $5 = m(-2) + 3 \Rightarrow -2m = 2 \Rightarrow m = -1$.
Subtract equations: $7y = 35 \Rightarrow y = 5$. $2x + 15 = 11 \Rightarrow x = -2$. [0.5 Mark]
Substitute $(-2, 5)$ in $y = mx + 3 \Rightarrow 5 = -2m + 3 \Rightarrow m = -1$. [0.5 Mark]
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🎯 Official CBSE Marking Scheme:
Finding intersection point $(-2, 5)$: 0.5 Mark
Solving for $m = -1$: 0.5 Mark
Correct Answer: $-1$
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