What is the common point of the lines y=20-x and 3x-2y-6=0 ?

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justaguide's profile pic

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

We have to find the common points of y=20-x and 3x-2y-6=0. This is equivalent to solving for x and y using the given equations.

We have y=20-x.

substitute this for y in 3x-2y-6=0

=> 3x - 2( 20 - x) - 6 = 0

=> 3x - 40 + 2x - 6 = 0

=> 5x - 46 = 0

=> x = 46/5

y = 20 - x = 20 - 46/5 = 54/5

Therefore the lines meet at the point (46/5 , 54/5)

giorgiana1976's profile pic

giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted on

To determine the common point of the lines, we'll have to solve the system formed form the equations of the lines.

y=20-x (1)

3x-2y-6=0 (2)

The solution of this system represents the coordinates of the intercepting point.

We'll solve the system using substitution method.

3x - 2(20-x) - 6 = 0 

We'll remove the brackets:

3x - 40 + 2x - 6 = 0

We'll combine like tems:

5x - 46 = 0

We'll add 46:

5x = 46

x = 46/5

We'll susbtitute x in (1) and we'll have:

y=20 - 46/5

y = (100-46)/5

y = 54/5

The coordinates of the intercepting point of the lines are (46/5 , 54/5).

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