Edexcel C1 — Question 22 8 marks

Exam BoardEdexcel
ModuleC1 (Core Mathematics 1)
Marks8
PaperDownload PDF ↗
TopicSimultaneous equations
TypeSimultaneous with substitution elimination
DifficultyModerate -0.8 Part (a) is a straightforward application of index laws (rewriting 9 as 3²) requiring minimal steps. Part (b) involves substituting a linear equation into a quadratic to solve simultaneous equations—a standard C1 technique with routine algebraic manipulation. The question is easier than average as it's highly procedural with clear pathways and no conceptual challenges beyond basic algebraic skills.
Spec1.02c Simultaneous equations: two variables by elimination and substitution1.06a Exponential function: a^x and e^x graphs and properties

  1. Given that \(3^x = 9^{y-1}\), show that \(x = 2y - 2\). [2]
  2. Solve the simultaneous equations \begin{align} x &= 2y - 2,
    x^2 &= y^2 + 7. \end{align} [6]

\begin{enumerate}[label=(\alph*)]
\item Given that $3^x = 9^{y-1}$, show that $x = 2y - 2$. [2]
\item Solve the simultaneous equations
\begin{align}
x &= 2y - 2,\\
x^2 &= y^2 + 7.
\end{align}
[6]
\end{enumerate}

\hfill \mbox{\textit{Edexcel C1  Q22 [8]}}