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

Given: Line passing through point of intersection of lines 2x + y = 5 and x + 3y + 8 = 0 and parallel to the line 3x + 4y = 7.

To find:

The equation of the required line.

Concept Used:

Point of intersection of two lines.

Explanation:

2x + y – 5 = 0 …… (i)

x + 3y + 8 = 0 …… (ii)

By solving equation (i) and (ii) ,By cross multiplication,

x , y

Point of intersection

Equation of line parallel to 3x + 4y – 7 = 0 is

3x + 4y + k = 0 …… (iii)

Equation (iii) passing through point of intersection of line.

k = 3

Hence, required equation of line is 3x + 4y + 3 = 0.

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