1MA0 Higher June 2013 Paper 2 Q25

25 Solve the simultaneous equations \[\begin{aligned} x^2 + y^2 &= 9 \\ x + y &= 2 \end{aligned}\] Give your answers correct to 2 decimal places. (6)

Mark scheme

Answer	Mark	Notes
\(x = 2.87\), \(y = -0.87\) and \(x = -0.87\), \(y = 2.87\)	6	M1 for \(x^2 + (2 - x)^2 = 9\) M1 for \(4 - 4x + x^2\) A1 for \(2x^2 - 4x - 5 = 0\) oe 3 term simplified quadratic M1 for a correct method to solve their quadratic Eg \(x = \dfrac{4 \pm \sqrt{16 - 4 \times 2 \times -5}}{4}\) A1 for \(x = 2.87\), \(y = -0.87\) or better A1 for \(x = -0.87\), \(y = 2.87\) or better Award marks for equivalent algebraic expressions. Apply the same scheme as above for \(y\) first.