Find the equation of the line passing through the intersection of the line $2 x + y = 5$ and $x + 3 y + 8 = 0$ and parallel to the line $3 x + 4 y = 7.$

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Solution

$2 x + y = 5$ and $x + 3 y + 8 = 0$

Intersection point of above lines is

$(\frac{23}{5}, \frac{- 21}{5})$

Required line is parallel to $3 x + 4 y = 7$

and passing through above point

So required line equation is

$y + \frac{21}{5} = \frac{- 3}{4} (x - \frac{23}{5})$

$20 y + 84 = - 15 x + 69$

$15 x + 20 y + 15 = 0$

$3 x + 4 y + 3 = 0$

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Find the equation of the line passing through the intersection of the line 2x+y=5 and x+3y+8=0 and parallel to the line 3x+4y=7.

2x+y=5 and x+3y+8=0 Intersection point of above lines is (235,−215) Required line is parallel to 3x+4y=7 and passing through above point So required line equation is y+215=−34(x−235) 20y+84=−15x+69 15x+20y+15=0 3x+4y+3=0

Find the equation of the line passing through the intersection of the line $2 x + y = 5$ and $x + 3 y + 8 = 0$ and parallel to the line $3 x + 4 y = 7.$