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

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To find the common point of the lines 2x+2y = 4....(1) and

x-3y =5..(2), we solve the equations by substitution.

Add 3y to both sides of eq (2).

x = 3y+5

We substitute x = 3y + 5 in th first equation, 2x+2y =4

2(3y +5) +2y = 4.

Open the brackects:

6y +10 = 4

Subtract 5:

6y =4-10 = -6

6y/6 = -6/6 = -1.

y= -1.

Put y = -1 in the first eq: x -3y = 5

x -3(-1) = 5

x = 5-3 = 2.

x = 2 and y =-1.

**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)}.**