The diagram shows the graph of $x^2 + y^2 = 30.25$ - Edexcel - GCSE Maths - Question 20 - 2021 - Paper 1

To find the points of intersection between the circle and the line defined by the equation $y - 2x = 1$, we can rearrange the equation to express y: $y = 2x + 1$.

Now we substitute this expression into the first equation: $x^2 + (2x + 1)^2 = 30.25$ Expanding this: $x^2 + (4x^2 + 4x + 1) = 30.25$ Combining like terms: $5x^2 + 4x + 1 - 30.25 = 0$ Thus: $5x^2 + 4x - 29.25 = 0$ Using the graph, at the intersections, we can estimate the values for x. From the graph, we can approximate two pairs of (x, y) values for the intersection points:

1. $x ext{ approximately } 2.2$, then substituting to find $y$: $y = 2(2.2) + 1 ext{ approximately } 5.4$. So, one estimated coordinate is $(2.2, 5.4)$.
2. $x ext{ approximately } -4.6$, then substituting to find $y$: $y = 2(-4.6) + 1 ext{ approximately } -8.2$. So, another estimated coordinate is $(-4.6, -8.2)$.