# 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.

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### 2 Answers

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)**

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=2x-1

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:

**A(1/3,-1/3)**