Edexcel C1 — Question 7 7 marks

Exam BoardEdexcel
ModuleC1 (Core Mathematics 1)
Marks7
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicSimultaneous equations
TypeSimultaneous with substitution elimination
DifficultyStandard +0.3 This is a standard C1 simultaneous equations question combining one linear and one quadratic equation. Students substitute the linear equation into the quadratic, leading to a straightforward quadratic to solve. While it requires algebraic manipulation and handling two solutions, it follows a well-practiced routine with no conceptual surprises, making it slightly easier than average.
Spec1.02c Simultaneous equations: two variables by elimination and substitution
Solve the simultaneous equations \begin{align} x - 3y + 7 &= 0
x^2 + 2xy - y^2 &= 7 \end{align} [7]
AnswerMarks Guidance
\(x - 3y + 7 = 0 \Rightarrow x = 3y - 7\)M1
sub. into \(x^2 + 2xy - y^2 = 7\)
\((3y - 7)^2 + 2(3y - 7) - y^2 = 7\)M1
\(y^2 - 4y + 3 = 0\)A1
\((y - 1)(y - 3) = 0\)M1
\(y = 1, 3\)A1
\(\therefore x = -4, y = 1\) or \(x = 2, y = 3\)M1 A1 (7) 
$x - 3y + 7 = 0 \Rightarrow x = 3y - 7$ | M1 |
sub. into $x^2 + 2xy - y^2 = 7$ | |
$(3y - 7)^2 + 2(3y - 7) - y^2 = 7$ | M1 |
$y^2 - 4y + 3 = 0$ | A1 |
$(y - 1)(y - 3) = 0$ | M1 |
$y = 1, 3$ | A1 |
$\therefore x = -4, y = 1$ or $x = 2, y = 3$ | M1 A1 | (7)
Solve the simultaneous equations
\begin{align}
x - 3y + 7 &= 0\\
x^2 + 2xy - y^2 &= 7
\end{align} [7]

\hfill \mbox{\textit{Edexcel C1  Q7 [7]}}
This paper (10 questions)
View full paper
Q1 3 Q2 4 Q3 6 Q4 6 Q5 6 Q6 7 Q7 7 Q8 9 Q9 13 Q10 14