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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
Solution
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
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