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Question
Show that the system 2x + 3y -1= 0 and 4x + 6y - 4 = 0 has no solution.
Solution
The given system is
2x + 3y – 1 = 0 ……(i)
4x + 6y – 4 = 0 ……(ii)
Here,` a_1 = 2, b_1 = 3, c_1 = -1, a_2 = 4, b_2 = 6 and c_2 = -4`
Now,
`(a_1)/(a_2) = 2/4 = 1/2`
`(b_1)/(b_2) = 3/6 = 1/2`
`(c_1)/(c_2) = (−1)/(−4) = 1/4`
Thus, `(a_1)/(a_2) = (b_1)/(b_2) ≠ (c_1)/(c_2 )` and therefore the given system has no solution.
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