Given a linear equation in two variables: 5x + 7y - 8 = 0, which of the following linear equations, along with the given equation, forms a system of linear equations having no solution?
Show answer & explanation
Correct answer: A
Explanation
The correct answer is option 1 i.e. 5x + 7y - 16 = 0.
If a1x + b1y + c1 = 0 and a2x + b2y + c2 = 0
The condition for no solution: a1/a2 = b1/b2 ≠ c1/c2
Given equation: 5x + 7y - 8 = 0 .....(1)
In option (1), 5x + 7y - 16 = 0 .....(2)
From equations (1) and (2), we get
a1 = 5, b1 = 7, c1 = - 8 and a2 = 5, b2 = 7, c2 = - 16
So, a1/a2 = b1/b2 because 5/5 = 7/7 = 1
Also, b1/b2 ≠ c1/c2 because 7/7 ≠ -8/-16
Therefore, the required equation is 5x + 7y - 16 = 0.