Verify if the lines are intercepting? x+y = 20 3x - 2y = 6

The lines x+y = 20 and 3x-2y= 6 must inersect as their
slopes are obviously looking different.

Slope of x+y = 20 
or y = 20-x (which is in y = mx+c , m is slope ) is
-1.

Slope of  of 3x-2y = 6 or -2y = -3x+6 ,  or y
=(3/2)x- 6/2 , is
3/2.

Intersection of the lines are the solution of the
equations:

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

3x-2y =
6..................(2)

Add 2*eq(1) and eq(2 ) . Then y gets
eliminated:

2x+3x = 2*20+6 =
46

5x=46

x = 46/5=
9.2.

Eq(3)*3 - Eq(2) eliminates
x:

3y- (-2y) = 3*20-6 = 56

5y
= 56

y = 54/5 = 10.4

Therefore
(x,y) = (9.2 , 10.4) are the coordinates of the point of intersection of the 2
lines.