At the common point of the two lines the values of x and y are the same. Therefore we can solve the two equations for x and y.

4x+8y=20 ...(1)

-4x+2y=-30...(2)

Add (1) and (2)

=> 10 y = -10

=> y = -10/ 10

=> y = -1

Substitute y = -1 in 4x+8y=20

=> 4x - 8 = 20

=> 4x = 28

=> x = 28/4

=> x = 7

**Therefore the common point is (7, -1)**

To find the common point of the lines 4x+8y=20 and -4x+2y=-30?

4x+8y=20..........(1)

-4x+2y=-30.......(2)

We add both equations:

=> 8y+2y = 20-30 = -10.

=> 10y = -10.

=> y = -10/10 = -1.

So y = -1 in (1):

4x + 8(-1) = 20.

4x = 20+8 = 28.

x = 28/4 = 7.

Therefore the common point is (x,y) = (7, -1).

The common point of the lines is the solution of the system of the given equations:

4x+8y=20 (1)

-4x+2y=-30 (2)

We'll add (1) + (2) and we'll get:

4x + 8y - 4x + 2y = 20 - 30

We'll combine and eliminate like terms:

10y = -10

We'll divide by 10:

y =-1

We'll substitute y in (1):

4x - 8 = 20

We'll add 8:

4x = 28

We'll divide by 4:

x = 7

**The coordinates of the intercepting point of the lines are (7 ; -1).**