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Question

For what value of $$k$$ does the system of equations $$x+2y=3, 5x+ky+7=0$$ have
no solution ? Also, show that there is no value of $$k$$ for which the given system of equations has infinitely many solutions.


Solution

no solution? also, show that the there is no value of $$k$$ for which the given system of equations has infinitely many solutions.
System has no solution:
$$\dfrac {a_1}{a_2}=\dfrac {b_1}{b_2}\neq \dfrac {c_1}{c_2}\Rightarrow \dfrac {1}{5}=\dfrac {2}{k}\neq \dfrac {-3}{7}$$
$$\therefore k=10$$
System has infinitely many solutions:
$$\dfrac {a_1}{a_2}=\dfrac {b_1}{b_2}=\dfrac {c_1}{c_2}$$
$$\dfrac {1}{5}=\dfrac {2}{k}=\dfrac {-3}{7}$$
Which is not at all possible.
$$1/5 \neq -3/7$$
$$K$$ has no value. 

Mathematics
RS Agarwal
Standard X

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