Solve simple linear-quadratic systems algebraically and graphically.
Solve a linear-quadratic system by substituting the line into the quadratic
Problem
Solve \(x^{2}+y=6\) and \(y=x\) by rearranging or substitution. Reduce the system to one quadratic in \(x\), solve all roots, and return the matching ordered pairs.
Big Picture
What this problem is really about
Because the second equation already says y equals x, substitution removes one variable immediately. We’ll replace y in the first equation with x, solve the resulting quadratic for all possible x-values, use the same value for y in each case, and verify both ordered pairs in the original system.
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