The equation of the line passing through the point of intersection of the line $4 x - 3 y - 1 = 0$ and $5 x - 2 y - 3 = 0$ and parallel to the line $2 x - 3 y + 2 = 0$ is .

x - 3 y = 1

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3 x - 2 y = 1

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7 x - 7 y - 1 = 0

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2 x - 3 y = 1

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Solution

The correct option is C $7 x - 7 y - 1 = 0$
Let equation of any straight line passing through the point of untersection of two given straight line be

$k (4 x - 3 y - 1) = (5 x - 2 y - 3) = 0$
$=> (4 k + 5) x - (3 k + 2) y - (k + 3) = 0 - - - - - - - - - - - - - - - (i)$
xx
If the straight be parallel to the straight to the straight line $2 x - 3 y + 2 = 0$
$\frac{4 k + 5}{2} = \frac{- 3 k - 2}{- 2}$
$=> - 8 k + 6 k = - 4 + 10$
$=> k = 3$
inserting the value of k in equation $(i)$
$=> (4 \times (- 3) + 5) x - (3 (- 3) + 2) - (- 4 + 3 = 0)$

$- 7 x + 7 y + 1 = 0$
$7 x - 7 y - 1 = 0$

This line is the equation of the required straight line

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The equation of the line passing through the point of intersection of the line 4x−3y−1=0 and 5x−2y−3=0 and parallel to the line 2x−3y+2=0 is .

The equation of the line passing through the point of intersection of the line $4 x - 3 y - 1 = 0$ and $5 x - 2 y - 3 = 0$ and parallel to the line $2 x - 3 y + 2 = 0$ is .