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Class 10 › Mathematics › Pair of Linear Equations in Two Variables
CBSE2026Class Class 10 · Mathematics1 Marks · Mcq✅ Verified
The value of k for which the pair of linear equations $kx-3y=5$, $4x-6y=10$ has infinitely many solutions, is:
A. 4
B. 3
C. 2
D. 1
✅ Answer & Solution
✅ Correct Answer: C
For infinitely many solutions of $a_1x+b_1y=c_1$ and $a_2x+b_2y=c_2$: $$\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}$$ Here $\frac{k}{4}=\frac{-3}{-6}=\frac{5}{10}$. Since $\frac{-3}{-6}=\frac{1}{2}$ and $\frac{5}{10}=\frac{1}{2}$, we need $\frac{k}{4}=\frac{1}{2} \Rightarrow k=2$.
