We recognize that this is a straight line intersecting a circle. (See more on the circle.)

We may have:

- no intersection point
- 1 intersection point
- 2 intersection points

We can simply substitute the right hand side of the first equation into the second equation:

x^{2}+ (x+ 1)^{2}= 25

This gives:

x^{2}+x^{2}+ 2x+ 1 = 252

x^{2}+ 2x− 24 = 0

x^{2}+x− 12 = 0(

x+ 4)(x− 3) = 0

So `x = −4` or `x = 3`.

This gives our intersecting points to be: `(−4, −3)` and `(3, 4)`.

Is it correct? The graph showing the line intersecting the circle is as follows:

Graphs of `y = x+1` and `x^2+y^2=25`: Intersection line and circle

We can see from the graph that our solutions `(−4, −3)` and `(3, 4)` are correct.

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