Find the coordinates of the point of intersection of the lines y = 3x - 2 and x + 3y = 1.

(A-level Maths)
Simultaneous equations:
1) y = 3x -2 2) x + 3y = 1
Substitute y = 3x - 2 into equation 2: x + 3y = 1x + 3(3x-2) = 1 1 markx + 9x - 6 = 1 Expand brackets 10x - 6 = 1 Solve equation 10x = 1 + 610x = 7 1 markx = 7/10 = 0.7 Divide everything by 10
Substitute x = 0.7 into equation 2): x + 3y = 10.7 + 3y = 13y = 1 - 0.73y = 0.3 y = 0.1
Coordinates intersect at (0.7, 0.1) 2 marks for both coordinates/final answer
Total: 4 marks