1MA0 Higher June 2014 Paper 2 Q26

26 Solve the equations \[\begin{aligned} x^2 + y^2 &= 36 \\ x &= 2y + 6 \end{aligned}\] (5)

Mark scheme

Working	Answer	Mark	Notes
\(y(5y + 24) = 0\) \(\dfrac{-24 \pm \sqrt{24^2}}{10}\)	\(x = 6\), \(y = 0\) \(x = -3.6\), \(y = -4.8\)	5	M1 for substitution for elimination eg \((2y + 6)^2 + y^2 = 36\) M1 (dep on M1) for expansion eg \(4y^2 + 12y + 12y + 36\) (3 out of 4 terms correct) A1 for \(4y^2 + 24y + 36 + y^2 = 36\) oe M1 for a correct attempt to solve a 2 or 3 term quadratic equation eg by factorising or correct substitution into a quadratic formula A1 for \(x = 6\), \(y = 0\) and \(x = -3.6\) oe, \(y = -4.8\) oe SC: B1 (if M0 scored) for all 4 values mis-associated or one correct pair of values.