1. Tardigrade
  2. Question
  3. Mathematics
  4. The straight lines x + 2y - 9 = 0, 3x + 5y - 5 = 0 and ax + by = 1 are concurrent if the straight line 35x - 22y + 1 = 0 passes through

Question Error Report

Thank you for reporting, we will resolve it shortly

Back to Question

Q. The straight lines x + 2y - 9 = 0, 3x + 5y - 5 = 0 and ax + by = 1 are concurrent if the straight line 35x - 22y + 1 = 0 passes through

Straight Lines

Solution:

Given equation of straingh lines are x + 2y - 9 = 0, 3x + 5y - 5 = 0 and ax + by - 1 = 0
They are concurrent if $\begin{vmatrix}1&2&-9\\ 3&5&-5\\ a&b&-1\end{vmatrix} = 0 $
$\Rightarrow \ - 5 + 5b - 2(- 3 + 5a) - 9(3b - 5a) = 0$
$\Rightarrow \ - 5 + 5b + 6 - 10a - 27b + 45a = 0$
$\Rightarrow \ 35a - 22b + 1 = 0$
Thus, given straight lines are concurrent if the straight line 35x - 22y + 1 = 0 passes through (a, b).