Equation of line Solution14



In this page equation of line solution14 we are going to see solution of each problem with detailed explanation of the worksheet slope of the line.

(13) Find the equation of the straight line joining the point of intersection of the lines 3 x – y + 9 = 0 and x + 2 y = 4 and the point of intersection of the lines 2 x + y – 4 = 0 and x – 2 y + 3 = 0.

Solution:  

Point of intersection of the lines 3 x – y + 9 = 0 and x + 2 y = 4

3 x – y = -9 ------- (1)

x + 2 y = 4 ------- (2)

(1) x 2 + (2) => 6 x – 2 y = - 18

                            x + 2y = 4    

                       ----------------

                          7x = -14

                            x = (-14)/7                                             

                            x = -2

Substitute x = -2 in the first equation

        3 (-2) – y = -9

            -6 – y = -9

                 - y = -9 + 6

              -y = -3

                y = 3       

Therefore the point of intersection of first two lines is (-2,3) 

Point of intersection of the lines 2 x + y – 4 = 0 and x – 2 y + 3 = 0.

2 x + y = 4  ------- (3)

x - 2 y = -3 ------- (2)

(1) x 2 + (2) => 4 x + 2 y = 8

                         x - 2y = -3    

                       --------------

                          5x = 5

                            x = 5/5                                             

                            x = 1

Substitute x = 1in the first equation

        2 (1) + y = 4

            2 + y = 4

                  y = 4 - 2

                  y = 2

Therefore the point of intersection of first two lines is (2 , 1)

Equation of the required line

(-2 , 3)   (2 , 1)

(y - y₁)/(y₂ - y₁) =(x - x₁)/(x₂ - x₁)

(y - 3)/(1 - 3) = (x - (-2))/(2 - (-2))

(y - 3)/(-2) = (x + 2)/(2 + 2)

(y - 3)/(-2) = (x + 2)/4

4 (y - 3) = -2 (x + 2)

4y – 12 = - 2 x – 4

2 x + 4 y – 1 2 + 4 = 0

2 x + 4 y – 8 = 0

Divided by 2=> x + 2 y – 4 = 0

equation of line solution14 equation of line solution14