Answer: (2/5, 9/5)
Step by step explanation:
To find the solutions, we are given the value of y in terms of x: y = 2x + 1. We can plug this into the circle equation to get:
(x - 1)^2 + (2x + 1 - 1)^2 = 1
Now, we can expand and simplify:
x^2 - 2x + 1 + (2x)^2 = 1
x^2 - 2x + 1 + 4x^2 = 1
5x^2 - 2x = 0
Now, we can factor:
x(5x - 2) = 0
And, using the zero product property, we get two equations which we can solve:
x = 0
5x - 2 = 0
5x = 2
x = 2/5
Since x is 0 in the first solution, we use the other solution and plug it into the equation y = 2x + 1 to find y:
y = 2(2/5) + 1
y = 4/5 + 1
y = 9/5
This means the coordinates of the point is (2/5, 9/5)
