Simultaneous with substitution elimination

A question is this type if and only if it requires algebraic manipulation to eliminate variables and form a single equation in one variable (often leading to quartic or higher degree).

10 questions · Standard +0.1

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Edexcel P1 2022 June Q6

7 marks Standard +0.3

6. In this question you must show all stages of your working. Solutions relying on calculator technology are not acceptable.

Given that $$2 x y - 3 x ^ { 2 } = 50$$ and $$y - x ^ { 3 } + 6 x = 0$$ show that $$2 x ^ { 4 } - 15 x ^ { 2 } - 50 = 0$$
Hence solve the simultaneous equations $$\begin{aligned} 2 x y - 3 x ^ { 2 } & = 50 \\ y - x ^ { 3 } + 6 x & = 0 \end{aligned}$$ Give your answers in fully simplified surd form. \includegraphics[max width=\textwidth, alt={}, center]{3cf69966-e825-4ff0-a6e8-c5dfdc92c53f-14_2257_52_312_1982}

Edexcel P1 2023 October Q8

7 marks Standard +0.8

In this question you must show all stages of your working.

\section*{Solutions relying on calculator technology are not acceptable.} The curve $C _ { 1 }$ has equation $$x y = \frac { 15 } { 2 } - 5 x \quad x \neq 0$$ The curve $C _ { 2 }$ has equation $$y = x ^ { 3 } - \frac { 7 } { 2 } x - 5$$

Show that $C _ { 1 }$ and $C _ { 2 }$ meet when $$2 x ^ { 4 } - 7 x ^ { 2 } - 15 = 0$$ Given that $C _ { 1 }$ and $C _ { 2 }$ meet at points $P$ and $Q$
find, using algebra, the exact distance $P Q$