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.
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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: a1a2=b1b2≠c1c2⇒15=2k≠−37
∴k=10
System has infinitely many solutions: a1a2=b1b2=c1c2 15=2k=−37 Which is not at all possible. 1/5≠−3/7 K has no value.