We recognize that this is a straight line intersecting a circle. (See more on the circle.)
We may have:
We can simply substitute the right hand side of the first equation into the second equation:
x2 + (x + 1)2 = 25
x2 + x2 + 2x + 1 = 25
2x2 + 2x − 24 = 0
x2 + 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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