For what value of k, the system of equations x + 2y = 3, 5x + ky + 7 = 0 has unique solution ?
For what value of k, the system of equations x + 2y = 3, 5x + ky + 7 = 0 has unique solution ?
A) k = 10
B) All real values except 10
C) All natural numbers except 10
D) Does not exist
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Correct option is (B) All real values except 10
Condition for unique solution of given system of equations is \(\frac{a_1}{a_2}\neq\frac{b_1}{b_2}.\)
\(\Rightarrow\) \(\frac15\neq\frac2k\) (By comparing given system of equations with standard form of equations)
\(\Rightarrow\) \(k\neq5\times2\)
\(\Rightarrow\) \(k\neq10\)
Hence, given system of equations has unique solution for all real values except 10.
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