O-LevelAdditional MathematicsSimultaneous equations4037/22 · May/June 2015 · Q55 Marks

Solve the simultaneous equations 2x² + 3y² = 7xy, x + y = 4.

Mark scheme

Marking points from the official mark scheme (May/June 2015). The mark or mark type is shown in brackets.

[M1] Substitution of either 4 – x or 4 – y into equation of curve and brackets expanded condone one sign error or slip in either equation of curve or expansion of brackets; condone omission of = 0, BUT 4-x or 4-y must be correct
[A1] 12x² - 52x + 48 [= 0] or 12y² - 44y + 32 [= 0] oe
[M1] Solve their 3-term quadratic dep on a valid substitution attempt
[A1] x = 4/3 and 3 isw or x = 8/3 y=8/3 not from wrong working
[A1] y = 8/3 and 1 isw or x=3 y=1 not from wrong working if no working, allow full marks for fully correct answer only.

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Topic: Simultaneous equations, O-Level Additional Mathematics (syllabus 4037). Structured question, 5 marks.
Source: O-Level Additional Mathematics, May/June 2015 Paper 2 Variant 2, question 5.

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