Question

What coordinate do lines 2/3x+1/6y=2/3 and 4x+y=4 meet?

Answer 1

The coordinates of the lines when both lines meets at point is ( 0, 0 )

Explanation:

Given as :

The two lines are

`(2)/(3)`x +
`(1)/(6)`y =
`(2)/(3)`

And 4 x + y = 4

The coordinate of the lines are obtained when the two lines intersect

Let the coordinate of intersection points are ( x , y )

Now , The first lines as

`(2)/(3)`x +
`(1)/(6)`y =
`(2)/(3)`

Or, Taking LCM we get ,

`(4x + y)/(6)` =
`(2)/(3)`

Cross multiplication both sides

Or, 3 × ( 4 x + y ) = 2 × 6

Or, 3 × 4 x + 3 × y = 12

Or, 12 x + 3 y = 12 ...........A

Other line is 4 x + y = 4

i.e 3 × ( 4 x + y ) = 3 × 4

or, 12 x + 3 y = 12 .........B

Solving both the line equations

(12 x + 3 y ) - ( 12 x + 3 y ) = 12 - 12

I.e x = 0 and y = 0

So coordinates are ( x , y ) = ( 0 , 0 )

Hence The coordinates of the lines when both lines meets at point is ( 0, 0 ) Answer