Pre-U Pre-U 9794/2 Specimen — Question 2 4 marks

Exam BoardPre-U
ModulePre-U 9794/2 (Pre-U Mathematics Paper 2)
SessionSpecimen
Marks4
TopicSimultaneous equations
TypeLine intersecting reciprocal curve
DifficultyStandard +0.3 This is a simultaneous equations problem combining linear and rational equations. While it requires substitution and algebraic manipulation beyond basic linear systems, the approach is straightforward: express x from the first equation, substitute into the second, and solve the resulting quadratic. The 4-mark allocation confirms it's slightly above routine but still a standard technique tested at A-level.
Spec1.02c Simultaneous equations: two variables by elimination and substitution

Solve the simultaneous equations $$x - 2y = 5,$$ $$\frac{4}{x} - \frac{2}{y} = 5.$$ [4]

AnswerMarks Guidance
Remove fractions: \(2(2y - x) = 5xy\) (⇒ \(xy = -2\))B1 Substitute for \(x\) (\(= 2y + 5\))
Remove fractions: $2(2y - x) = 5xy$ (⇒ $xy = -2$) | B1 | Substitute for $x$ ($= 2y + 5$) | M1 | Obtain $2y^2 + 5y + 2 = 0$ | A1 | Solutions $(x, y) = (1, -2)$ and $(4, -0.5)$ | A1 | 4 marks
Solve the simultaneous equations
$$x - 2y = 5,$$
$$\frac{4}{x} - \frac{2}{y} = 5.$$ 
[4]

\hfill \mbox{\textit{Pre-U Pre-U 9794/2  Q2 [4]}}