alleryIf the system of equations $x + 2y = 3$ and $5x + ky + 7 = 0$ has no solution, then the value of $k$ is:
A2
B5
C10
D15
Answer & Solution
Correct answer: C. 10
1. For no solution (parallel lines): $a_1/a_2 = b_1/b_2 \ne c_1/c_2$.
2. Here $a_1/a_2 = 1/5$ and $b_1/b_2 = 2/k$.
3. Equating them gives $1/5 = 2/k \Rightarrow k = 10$.
4. Also $c_1/c_2 = (-3)/7 \ne 1/5$, which holds true. Thus $k = 10$.
_Source: NCERT Class 10 Mathematics, Ch3 'Pair of Linear Equations in Two Variables'_
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