For what value of m will the system of equations 17x + my + 102 = 0 and 23x + 299y + 138 = 0 have infinite number of solutions?

Solution (By Examveda Team)

$$\eqalign{ & 17x + my + 102 = 0 \cr & 23x + 299y + 138 = 0 \cr & {\text{Infinite solution}} \cr & \frac{{{a_1}}}{{{a_2}}} = \frac{{{b_1}}}{{{b_2}}} \cr & \frac{{17}}{{23}} = \frac{m}{{299}} \cr & m = \frac{{17 \times 299}}{{23}} = 221 \cr} $$