What is the common point of the lines y=20-x and 3x-2y-6=0 ?
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)
To determine the common point of the lines, we'll have to solve the system formed form the equations of the lines.
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).