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