Solve simple linear-quadratic systems algebraically and graphically.
Check a candidate point in a linear-quadratic system
Problem
Test whether \((1,1)\) solves \(y=x^{2}\) and \(y=4x-3\). Substitute \(x\) and \(y\) into each equation separately, state both truth values, and give the system-solution verdict.
Big Picture
What this problem is really about
A candidate point solves a system only if the same coordinates satisfy every equation. We’ll preserve the coordinate roles, substitute x and y into the quadratic and line separately, record both truth values, and combine them with the system’s logical-and requirement to reach the verdict.
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