Moderate -0.8 This is a straightforward C1 question requiring substitution to form a quadratic equation, then factorising or using the formula. Part (ii) simply asks for interpretation of two solutions (line intersects curve at two points). Below average difficulty as it's a standard textbook exercise with no problem-solving insight required.
3. (i) Solve the simultaneous equations
$$\begin{aligned}
& y = x ^ { 2 } - 6 x + 7 \\
& y = 2 x - 9
\end{aligned}$$
(ii) Hence, describe the geometrical relationship between the curve \(y = x ^ { 2 } - 6 x + 7\) and the straight line \(y = 2 x - 9\).
3. (i) Solve the simultaneous equations
$$\begin{aligned}
& y = x ^ { 2 } - 6 x + 7 \\
& y = 2 x - 9
\end{aligned}$$
(ii) Hence, describe the geometrical relationship between the curve $y = x ^ { 2 } - 6 x + 7$ and the straight line $y = 2 x - 9$.\\
\hfill \mbox{\textit{OCR C1 Q3 [5]}}