Question

Find the equation of a line passing through the intersection of x + 3y = 6 and 2x - 3y = 12 and parallel to the line 5x + 2y = 10

Answer 1

x + 3y = 6...........(1)

2x - 3y = 12..........(2)

Adding (1) and (2), we get

3x = 18

⇒ x = 6

And y = 0

Point of intersection of given line is (6,0)

Slope of 5x + 2y = 10 is `(-5)/2`

Slope of required line is `(-5)/2`

Equation of required line is `("y" - "y"_1)/("x" - "x"_1)` = slope

`("y" - 0)/("x" - 6) = (-5)/2`

⇒ -5x + 30 = 2y

⇒ 5x + 2y - 30 = 0