Solve simple linear-quadratic systems algebraically and graphically.
Solve a linear-quadratic system when the line is horizontal or vertical
Problem
Solve the system \(y=x^{2}-1\) and \(y=3\). Substitute the horizontal-line value, solve both \(x\)-branches, and report every intersection as an ordered pair.
Big Picture
What this problem is really about
A horizontal line fixes the y-coordinate of every possible intersection. We’ll substitute that fixed output into the quadratic, isolate the square, keep both square-root branches, and pair each resulting x-value with the line’s y-value to form and check the complete solution set.
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