Determine the common point of the lines 2x+y-5=0 and -3x+4y-9=0.

To determine the crossing point of the 2 lines, we have to solve the system formed from their equations:

2x+y=5 (1)

-3x+4y=9 (2)

We'll multiply the relation (1) by 3 and the relation (2), by 2, and after that, we'll add (1) to (2). We'll obtain:

6x+3y-6x+8y = 15 + 18

After reducing similar terms, we'll get:

11y = 33

y = 33/11

y=3

We'll substitute y by 3, into the relation (1):

2x+3 = 5

2x = 5-3

2x = 2

x = 1

The crossing point is A (1,3).