How to find the intersection point of the lines y=1008-2x and y= -x ?

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justaguide's profile pic

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

We have to find the point of intersection of y = 1008 - 2x and y = -x

Substitute y = -x in y = 1008 - 2x

=> -x = 1008 - 2x

=> 2x - x = 1008

=> x = 1008

Therefore the point of intersection is (1008, -1008)

giorgiana1976's profile pic

giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted on

The main property of an intercepting point is: it's coordinates verify the equations of the curves that are intercepting.

If M(x,y) is the intersection point for the given lines, that means that the values for it's coordinates are the solution of the system formed by the equations of the lines.

So, in order to find out the values of the coordinates of the intercepting point, we have to solve the system:

Since the 2nd equation is y  =-x, we'll substitute it into the first equation:

-x = 1008 - 2x

We'll move all terms in x to the left side and we'll keep the numbers to the right side:

2x - x = 1008

x = 1008

But x = -y

y=-1008

The  values of the coordinates of the intercepting point are : M(1008,-1008).

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