Question

Find the equation of the straight line which passes through the point of intersection of the straight lines x + y = 8 and 3x - 2y + 1 = 0 and is parallel to the straight line joining the points (3, 4) and (5, 6).

• A. x - y + 2 = 0
• B. x + y - 2 = 0
• C. 3x - 4y + 8 = 0
• D. none of these

Answer 1

The correct option is A x - y + 2 = 0

Solving x + y = 8 and 3x - 2y + 1 = 0, we get the point of intersection.
$\therefore$ The point of intersection is (3, 5).
Now, the equation of the line joining the points (3, 4) and (5, 6) is $(y-4)=\frac{(6-4)}{(5-3)}(x-3)\Rightarrow x-y+1=\mathrm{0....}\left(1\right)$
$\therefore$ The equation of the line parallel to the line x - y + 1 = 0 is
x - y + c = 0..........(2)
Where c is an arbitrary constant. If the line passes through the point (3, 5) then
3 - 5 + c = 0 or c = 2
Hence from (2), the required equation of the line is x - y + 2 = 0.