Verify if the lines are intercepting: x+y = 8 4x-2y = 12

To verify whether the lones are
intercepting.

x+y = 8

4x-2y =
12.

Two lines are intersecting if they are not
parallel.

The given line are not parallel as the ratio of
coefficiet x and  y of 1st line is not that of the other line. Or their slope are
different.

Let us solve the equations and the solution in x
and y coordinates are the point of intersection of the 2
lines.

x+y = 8 an

4x-2y =
12.

Eq(1)*2 + eq(2) elimintes
y:

(x+y)*2 +(4x-2y) = 8*2+12 =
28

6x  = 28. x = 28/6 =
14/3.

So from (1) x+y= 8. Or y = 8-x = 8-14/3 =
10/3.

So (x,y) = (14/3 , 10/3) is the point of intersection
of the lines.

Or