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At the point of intersection of the lines the x and y co-ordinates are the same
We have y = -x +14 and y = 4x - 11.
Equating the y-coordinates ,we get
-x + 14 = 4x - 11
=> 5x = 25
=> x = 5
y = -x + 14 = -5 + 14 = 9
The point of intersection of the two lines is ( 5, 9)
To determine the intercepting point of the given lines, we'll have to solve the system of equations of the lines.
We'll re-write the equations, keeping the variables x and y to the left side.
In the first equation, we'll shift x to the left, changing it's sign:
x + y = 14 (1)
In the second equation, we'll shift x to the left and we'll re-arrange the terms:
4x - y = 11 (2)
We'll solve the system using substitution:
x = 14 - y (3)
We'll replace x in the 2nd equation by the expression from (3):
4(14 - y) - y = 11
We'll remove the brackets:
56 - 4y - y = 11
-5y = 11 - 56
-5y = -45
We'll divide by -5:
y = 9
We'll substitute y in (3):
x = 14 - 9
x = 5
The solution of the system represents the intercepting point of the lines, whose coordinates are given by the pair: (5 ; 9).
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