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Question
Write the number of solutions of the following pair of linear equations:
x + 3y – 4 = 0, 2x + 6y – 7 = 0.
Solution
The given pair of linear equations are
x + 3y – 4 = 0 ……(i)
2x + 6y – 7 = 0 ……(ii)
Which is of the form `a_1x + b_1y + c_1 = 0 and a_2x + b_2y + c_2 = 0`, where
`a_1 = 1, b_1 = 3, c_1 = -4, a_2 = 2, b_2 = 6 and c_2 = -7`
Now
`(a_1)/(a_2) = 1/2`
`(b_1)/(b_2) = 3/6 = 1/2`
`(c_1)/(c_2) = (−4)/(−7) = 4/7`
`⇒ (a_1)/(a_2) = (b_1)/(b_2) ≠ (c_1)/(c_2)`
Thus, the pair of the given linear equations has no solution.
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