Question

2." Find the equation of the line through the intersection of lines x + 2y - 3 = 0 and

4x - y + 7 = 0 and which is parallel to 5x + 4y – 20 = 0
(Ans. 15x + 12y - 7 = 0)

Answer 1

Explanation:

hello :

1 ) calculate point the intersection of lines lines ;

x + 2y - 3 = 0 ...(*)

4x - y + 7 = 0...(**)

solve this system : multiply (**) by 2

x+2y-3 = 0 ....(*)

8x-2y +14 = 0 ..(***)

add (*) and (***) : 9x+11 =0

9x = -11 so : x = -11/9 put this value in (**):

4(-11/9) - y + 7 = 0

y = 7-44/9 = 19/9

the point is A(-11/9 ; 19/9)

2) my line is parallel to 5x + 4y – 20 = 0

so : same slope now calculate the slope of the line :5x + 4y – 20 = 0

4y = -5x+20

y = -5/4 x + 5 the slope is : -5/4

an equation is : y - 19/9 = -5/4(x+11/9)

y -19/9 = -5/4 x - 55/36

multiply by 36 : 36y-76 = -45 x -55

36y +45x -21 =0 divid by 3 :

12y+15x -7 =0

conclusionn : 15x+12y -7 =0

same (Ans. 15x + 12y - 7 = 0) .... thanks