Question

The equation of the line passing throught the point of intersection of the lines x+y-5=0,2x-y+4=0 and having intercepts numerically equal

Answer 1

Answer:

x + y = 5

Step-by-step explanation:

For point of intersection:  when x + y - 5 = 0 and 2x - y + 4 = 0 meet is the point when both x(s) are and both y(s) are same.  Adding both:

x + y - 5 = 0  

2x - y + 4 = 0

3x     - 1    = 0         ⇒ x = 1/3

Thus,

x + y - 5 = 0      ⇒ y = 5 - (1/3) = 14/3

Point of intersection is (x , y) = (1/3 , 14/3)

Using intercept form:  (intercepts are same ⇒ a = b)

equation is  x/a + y/b = 1

     ⇒ x/a + b/a = 1     [a = b]

     ⇒ x + b = a

      ⇒ 1/3 + 14/3 = a

      ⇒ a = 5

∴ Equation is x + b = a  

                      x + y = 5