Pair of Linear Equations in Two Variables
RD Sharma
CBSE
Grade 10
Question:
Find the value of $k$ for which the pair of equations $2x + 3y = 7$ and $(k - 1)x + (k + 2)y = 3k$ has infinitely many solutions.
Step-by-Step Solution
Key Concept: $\\dfrac{2}{k-1} = \\dfrac{3}{k+2} = \\dfrac{7}{3k}$.
$\\dfrac{2}{k-1} = \\dfrac{3}{k+2} \Rightarrow 2(k + 2) = 3(k - 1) \Rightarrow 2k + 4 = 3k - 3 \Rightarrow k = 7$. [1.0 Mark]
Check 3rd ratio: $\\dfrac{7}{3(7)} = \\dfrac{1}{3}$. Also $\\dfrac{2}{7-1} = \\dfrac{2}{6} = \\dfrac{1}{3}$. Verified! $k = 7$. [1.0 Mark]
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🎯 Official CBSE Marking Scheme:
Solving $k = 7$: 1.0 Mark
Verifying third ratio: 1.0 Mark
Correct Answer:
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