To find the exact solution to the system of equations given by y = 6075x and y = 4x + 1, we can set the two equations equal to each other since they both represent y.
So we set:
6075x = 4x + 1
Next, we will rearrange the equation to isolate x. First, let’s get all terms containing x on one side:
6075x – 4x = 1
This simplifies to:
6071x = 1
Now, divide both sides by 6071:
x = 1/6071
Now that we have the value of x, we can substitute it back into either of the original equations to find y. Let’s use the first equation:
y = 6075(1/6071)
y = 6075/6071
Consequently, the point that satisfies both equations is:
(x, y) = (1/6071, 6075/6071)
This means the exact solution to the system is:
(1/6071, 6075/6071).