Question : For what value of m will the system of equations $17x + my + 102 = 0$ and $23x + 299y + 138 = 0$ will have an infinite number of solutions?
Option 1: 221
Option 2: 223
Option 3: 220
Option 4: 219
Correct Answer: 221
Solution :
Given: $17x + my + 102 = 0$ and $23x + 299y + 138 = 0$
$a_1x + b_1y + c_1 = 0$
$a_2x + b_2y + c_2 = 0$
The condition for an infinite number of solutions is $\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}$
According to the question,
$\frac{17}{23}=\frac{m}{299}$
⇒ $m=\frac{17×299}{23}$
⇒ $m= 17 × 13$
⇒ $m= 221$
Hence, the correct answer is 221.
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