f(x)=2x-1, g(x)=-4x+1. Find the coordinates of the point found at the intersection of  f(x) and g(x) curves.

neela | Student

Let x1 and y1 be the  coordinates  of the intersection point

of the functions ,  f(x)=2x-1 and g(x)=-4x+1. Then the cordinates  of the intersecting point ,(x1, y1) nturally satisfy both equations. Therefore,

y1=2x1-1         (1)

y1=-4x1+1       (2)

Solve these simulaneous equations:

Equation(1)*2+ equation(2) gives:

2y1+y1=-2+1=-1==> 3y1=-1. or y1=-1/3

Substitute y1 =-1/2 in  Eq (1): -1/3=2x1-1=> 2x1=1-1/3=2/3==>  x1=1/3.

Therefore, the intersection point  f(x) and g(x) is:

(x1,y1) = (1/3,-1/3)



giorgiana1976 | Student

In order to find out the coordinates of the intersection point, we have to say that it's coordinates have to verify the expression of each function, in the same time.

So, in conclusion, we have to solve the system formed by the expression of the 2 functions:


y=-4x+1, 2x-1=-4x+1, 2x+4x=1+1, 6x=2, x=1/3

y=2x-1, y=2*1/3-1, y=-1/3

So, the coordinates of the intersection point are: