Solve the following simultaneous equations. 4x² + 3xy + y² = 8 xy+4 = 0

Mark scheme

Marking points from the official mark scheme (May/June 2021). The mark or mark type is shown in brackets.

1. M1 Correctly eliminates x or y e.g. 4x² + 3x(-4/x) + (-4/x)² = 8 oe or 4(-4/y)² + 3(-4/y)y + y² = 8 oe
2. A1 Rearranges to a 3-term quadratic in x² or y² soi e.g. 4x⁴ - 20x² + 16 = 0 or y⁴ - 20y² + 64 = 0
3. M1 Factorises or solves their 3-term quadratic expression or equation for x² or y² soi : (x² - 1)(x²-4) or (y² – 16)(y² – 4)
4. A1 x² =1, x² = 4 oe, nfww or y² =16, y² = 4 oe, nfww
5. A2 A1 for all 4 x values or all 4 y values x = ±1 x = ±2 y = ±4 y = ±2 oe, nfww