Find the common point of the lines 2x+2y=4 and x-3y=5

To determine the intercepting point of the
given lines, we'll have to solve the system formed by the equations of the
lines

We'll try to solve the
system using substitution method.

x - 3y =
5

x = 5 + 3y (1)

We'll
substitute (1) in the second equation of the system:

2x +
2y = 4

We'll divide by 2:

x +
y = 2

(5 + 3y) + y = 2

We'll
remove the brackets:

5 + 3y + y =
2

We'll combine like terms:

5
+ 4y = 2

We'll subtract 5:

4y
= -3

We'll divide by
4:

y =
-3/4

We'll substitute y in
(1):

x = 5 - 9/4

x =
(20-9)/4

x =
11/4

The solution of the
system is {(11/4;-3/4)}.