Edexcel C1 — Question 4 7 marks

Exam BoardEdexcel
ModuleC1 (Core Mathematics 1)
Marks7
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicSimultaneous equations
TypeLine intersecting quadratic curve
DifficultyModerate -0.3 This is a standard C1 simultaneous equations question combining a linear and quadratic equation. Students substitute the linear equation into the quadratic, expand to get a quadratic in one variable, solve it, then find corresponding y-values. While it requires multiple steps and careful algebra, it follows a well-practiced routine with no conceptual difficulty or novel insight required, making it slightly easier than average.
Spec1.02c Simultaneous equations: two variables by elimination and substitution

Find the pairs of values \((x, y)\) which satisfy the simultaneous equations $$3x^2 + y^2 = 21$$ $$5x + y = 7$$ [7]

AnswerMarks Guidance
\(5x + y = 7 \Rightarrow y = 7 - 5x\)M1
sub. into \(3x^2 + y^2 = 21\)M1
\(3x^2 + (7 - 5x)^2 = 21\)
\(2x^2 - 5x + 2 = 0\)A1
\((2x - 1)(x - 2) = 0\)M1
\(x = \frac{1}{2}, 2\)A1
\(\therefore \left(\frac{1}{2}, \frac{9}{2}\right)\) and \((2, -3)\)M1 A1 (7 marks)
$5x + y = 7 \Rightarrow y = 7 - 5x$ | M1 |
sub. into $3x^2 + y^2 = 21$ | M1 |
$3x^2 + (7 - 5x)^2 = 21$ | |
$2x^2 - 5x + 2 = 0$ | A1 |
$(2x - 1)(x - 2) = 0$ | M1 |
$x = \frac{1}{2}, 2$ | A1 |
$\therefore \left(\frac{1}{2}, \frac{9}{2}\right)$ and $(2, -3)$ | M1 A1 | (7 marks)
Find the pairs of values $(x, y)$ which satisfy the simultaneous equations
$$3x^2 + y^2 = 21$$
$$5x + y = 7$$
[7]

\hfill \mbox{\textit{Edexcel C1  Q4 [7]}}