Find the coordinates of the points of intersection of the curve 4 + 5/y + 3/x = 0 and the line y = 15x + 10.

Mark scheme

Marking points from the official mark scheme (May/June 2016). The mark or mark type is shown in brackets.

1. [M1] Eliminates y e.g. 4 + 5/(15x+10) + 3/x = 0 or eliminates x e.g. 4 + 5/y + 3/((y-10)/15) = 0 allow even after incorrect rearrangement of the equation of the curve (dependent on resulting equation still in terms of x and y); condone substitution of e.g. (y+10)/15
2. [M1] Rearrange to a 3-term quadratic 60x² + 90x + 30 = 0 oe or 4y² + 10y - 50 = 0 oe condone sign slips/arithmetic slips
3. [A1]
4. [M1] Factorise or solve 3-term quadratic
5. [A1] x = -1/2, x = -1 isw or y = 2, y = -5
6. [A1] y = 2, y = -5 isw or x = -1/2, x = -1 If final A marks not awarded then A1 for a correct x, y pair