Given the lines:
f(x)= 2x - 1
In order to find a point on both lines, then we need to determine where the lines intersects.
To find intersection points we need to determine x values such that f(x) = g(x).
==> 2x-1 = -4x + 1
Now we will solve by grouping similar terms.
==> 6x = 2
==> x = 2/6 = 1/3
Now we will determine g(1/3) = f(1/3) = 2*1/3 -1 = -1/3
==> Then, the point of intersection is ( 1/3, -1/3)
If the point is located on the given lines, it means that we talk about the intercepting point of the lines.
In order to find out the coordinates of the intercepting 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:
We'll move all terms in x to the left side and the numbers alone, to the right side.
We'll combine like terms:
Now, we'll substitute x in any of the given equations:
So, the coordinates of the intersection point are:(1/3,-1/3)