4400 Higher June 2004 Paper 4 Q21
21 Solve the simultaneous equations
\[2x + y = 6\] \[x^2 + y^2 = 20\](7)
| Scheme | Marks |
|---|---|
| \(y = 6 - 2x\) | M1 |
| \(x^2 + (6 - 2x)^2 = 20\) | M1 |
| \(x^2 + 36 - 24x + 4x^2 = 20\) | M1 |
| \(5x^2 - 24x + 16 = 0\) | A1 |
| \((5x - 4)(x - 4) = 0\) | M1 |
| \(x = 4\) and \(x = \frac{4}{5}\) oe | A1 |
| \(x = \frac{4}{5}\), \(y = 4\frac{2}{5}\) oe and \(x = 4\), \(y = -2\) | A1 |
| (7) | |
| (7 marks) |
Notes
M1: for making \(y\) (or \(x\)) the subject
M1: for substitution
M1: for correct expansion
A1: cao
A1: Must be in pairs
One pair only, by trial & improvement, or without working, M0A0