Q. 84.0( 5 Votes )
Find the equation of the line passing through the point of intersection of the lines 4x – 7y – 3 = 0 and 2x – 3y + 1 = 0 that has equal intercepts on the axes.
Answer :
Given:
4x − 7y − 3 = 0 … (1)
2x − 3y + 1 = 0 … (2)
To find:
Equation of line passing through the point of intersection of lines.
Concept Used:
Point of intersection of two lines.
Explanation:
Solving (1) and (2) using cross - multiplication method:
⇒ x = - 8 , y = - 5
Thus, the point of intersection of the given lines is ( - 8, - 5).
Now, the equation of a line having equal intercept as a is 
This line passes through ( - 8, - 5)
⇒ - 8 - 5 = a
⇒ a = - 13
Hence, the equation of the required line is 
or x + y + 13 = 0
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