Question

find the equation of line passing through yhe point of intersection of line x+y-2=0 and 2x-3y +4=0 parallel to x axis​

Answer 1

Answer:

First we solve the given equations of the two lines for a point in the required line.

From x + y - 2 = 0, let y = 2 - x.

Then,

2x - 3y + 4 = 0

2x - 3(2 - x) + 4 = 0

5x - 2 = 0

x = 2 / 5

And,

y = 2 - x = 2 - (2 / 5) = 8 / 5

So the point (2/5, 8/5) lies in the required line.

Since its x intercept is 3, we have another point, (3, 0).

Now we apply two point formula.

(y - 0) / (x - 3) = (8/5 - 0) / (2/5 - 3)

y / (x - 3) = (8/5) / (- 13/5)

y / (3 - x) = 8 / 13

13y = 8 (3 - x)

13y = 24 - 8x

8x + 13y - 24 = 0