determine the coordinates of two points on the plane with equation 5x + 4y - 3z = 6

Answer 1

pick any values for two of the variables, and calculate the third coordinate.

z = (6-5x-4y)/-3
so, if x=1 and y=10, z=13 and (1,10,13) is on the plane.

using similar expressions for x and y, you can pick points using x,z or y,z.

Answer 2

y = 6, z = 6

5x + 4(6) - 3(6) = 6
5x + 24 - 18 = 6
5x = 0
x = 0
so (0,6,6) is a point on the plane.

is this correct??