Question : For what value of m will the system of equations 18x – 72y + 13 = 0 and 7x – my – 17 = 0 have no solution?
Option 1: 28
Option 2: 24
Option 3: 9
Option 4: 12
Correct Answer: 28
Solution :
To have no solution, the two equations should represent parallel lines.
For a
1
x + b
1
y + c
1
= 0 and a
2
x + b
2
y + c
2
= 0, to be parallel lines $\frac{a_1}{a_2}=\frac{b_1}{b_2}\neq\frac{c_1}{c_2}$ this formula must satisfy.
18x – 72y + 13 = 0---(1)
7x – my – 17 = 0---(2)
So, $\frac{18}{7}=\frac{-72}{-m}\neq\frac{13}{-17}$
$⇒18m = 72×7$
$\therefore m =28$
Hence, the correct answer is 28.
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