Q. 164.8( 6 Votes )
Find the equation of the line passing through the intersection of the lines 2x + y = 5 and x + 3y + 8 = 0 and parallel to the line 3x + 4y = 7.
Answer :
Given: Line passing through point of intersection of lines 2x + y = 5 and x + 3y + 8 = 0 and parallel to the line 3x + 4y = 7.
To find:
The equation of the required line.
Concept Used:
Point of intersection of two lines.
Explanation:
2x + y – 5 = 0 …… (i)
x + 3y + 8 = 0 …… (ii)
By solving equation (i) and (ii) ,By cross multiplication,
⇒ x 
, y
Point of intersection 
Equation of line parallel to 3x + 4y – 7 = 0 is
3x + 4y + k = 0 …… (iii)
Equation (iii) passing through point of intersection of line.
⇒ 
⇒ k = 3
Hence, required equation of line is 3x + 4y + 3 = 0.
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