determine the coordinates of two points on the plane with equation 5x + 4y - 3z = 6
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.
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??
To determine the coordinates of two points on the plane with equation 5x + 4y - 3z = 6, we can set one of the variables to a constant value and solve for the other two variables.
Let's arbitrarily set z = 0 and solve for x and y:
5x + 4y - 3(0) = 6
5x + 4y = 6
To make the calculation easier, let's set y = 0:
5x + 4(0) = 6
5x = 6
x = 6/5
So, the first point on the plane is (6/5, 0, 0).
Now, let's set x = 0 and solve for y and z:
5(0) + 4y - 3z = 6
4y - 3z = 6
Again, let's set z = 0:
4y - 3(0) = 6
4y = 6
y = 6/4
y = 3/2
The second point on the plane is (0, 3/2, 0).
Therefore, the coordinates of two points on the plane 5x + 4y - 3z = 6 are (6/5, 0, 0) and (0, 3/2, 0).