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

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neela's profile pic

neela | High School Teacher | (Level 3) Valedictorian

Posted on

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.

giorgiana1976's profile pic

giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted on

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)}. 

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