Higher June 2017 Paper 1 Q20

20 Solve algebraically the simultaneous equations

\(x^2 + y^2 = 25\)
\(y - 3x = 13\) (5)

Mark scheme

Answer	Mark	Notes
\(x = -\dfrac{24}{5}\), \(y = -\dfrac{7}{5}\) \(x = -3\), \(y = 4\)	M1	for substitution of a rearrangement of \(y - 3x = 13\) e.g. \((3x + 13)^2 + x^2 = 25\)
	M1	(dep M1) for expansion of bracket after substitution (at least 3 terms correct out of the 4 terms) e.g. \(9x^2 + 39x + 39x + 169\)
	M1	for forming quadratic ready for solving e.g. \(10x^2 + 78x + 144\ (= 0)\)
	M1	for factorising e.g. \((5x + 24)(x + 3)\ (= 0)\) oe
	A1	\(x = -\dfrac{24}{5}\), \(y = -\dfrac{7}{5}\) and \(x = -3\), \(y = 4\) SC: B1 (if M0) for all 4 values mis-associated or one correct pair of values or values given as coordinates.