Find the equation of the straight line passing through the point of intersection of the lines 2x + y – 3 = 0 and 5x + y – 6 = 0 and parallel to the line joining the points (1, 2) and (2, 1).

Here it is given that the straight line passing through the point of intersection of the lines 2x + y – 3 = 0 and 5x + y – 6 = 0 and parallel to the line joining the points (1, 2) and (2, 1).

As the straight line passes through the point of intersection of the lines 2x + y – 3 = 0 and 5x + y – 6 = 0 , we should find the intersection point by solving these equations:

i.e –3x = –3

⇒ x = 1

Substitute x = 1 in 2x + y–3 = 0

We get,2(1) + y–3 = 0

⇒ y–1 = 0

⇒ y = 1

Therefore , the intersection point is (1,1).

As the line passing through(1,1) is parallel to the line segments

joining the points (1, 2) and(2, 1),their slopes are equal.

Slope of the line joining the points (1, 2) and(2, 1) is

⇒

Hence the equation of the line passing through the point (1,1) with slope m equal to –1 is

(y–y1) = m(x–x1)

⇒ (y–1) = –1(x–1)

⇒ y–1 = –x + 1

⇒ y–1 + x–1 = 0

⇒ x + y–2 = 0