Question

Find the point of intersection of the pair of straight lines.

10x - 4y = 43

-3x - 3y = -15

(x, y) = ( , )

Answer 1

(x,y) = (
`(9)/(2)`,
`(1)/(2)`)

Explanation:

We have to find point of intersection of two lines.

the given equations of line are:

10x - 4y = 43 - (1)

-3x - 3y = -15 - (2)

Multiplying the first equation by 3 we have:

(10x - 4y = 43)×3 = 30x - 12 y = 129 - (3)

Multiplying second equation by 10 we have :

(-3x - 3y = -15)×10 = -30x -30y = -150 - (4)

Now, adding equation (3) and (4) we have:

-42y = -21

⇒ y =
`(1)/(2)`

Now, putting this value of y in equation (1), we have

10x - 2 = 43

⇒ 10x = 45

⇒x =
`(9)/(2)`

Hence, the intersection of given two lines is (x,y) = (
`(9)/(2)`,
`(1)/(2)`)