Find the value of k for which the system of equations 6x + 7y = 0, kx + 21y = 0 has infinitely many solutions. ___

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Solution

The given system is of the form a1 x + b1 y = 0, a2 x + b2 y = 0

$a_{1}$ = 6, $a_{2}$ = k, $b_{1}$ = 7, $b_{2}$ = 21

If the system has infinitely many solutions.

$\frac{a_{1}}{a_{2}}$ = $\frac{b_{1}}{b_{2}}$

$\frac{6}{k}$ = $\frac{7}{21}$

k =18

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