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

let x=0, y=0, then z= -2 ---> (0,0,-2)

let x=1, y=0, then z = -1/3 -- (1,0,-1/3)

let two of the variables be anything you want, then solve for the third.

Just noticed that you had posted this before and Steve had answered you.

Please check your earlier posts before re-posting the same question again, to avoid unnecessary duplication of our efforts.
http://www.jiskha.com/display.cgi?id=1339787586

To determine the coordinates of two points on the plane with equation 5x + 4y - 3z = 6, we need to choose values for two of the variables and solve for the third variable.

Let's arbitrarily choose x = 0 and y = 0, and then solve for z.

By substituting x = 0 into the equation, we have:
5(0) + 4y - 3z = 6
4y - 3z = 6

Now let's choose y = 0 and solve for z.

By substituting y = 0 into the equation, we have:
5x + 4(0) - 3z = 6
5x - 3z = 6

Now we have a system of two linear equations with two variables. Let's solve it using any method, such as substitution or elimination.

First, let's solve for z in the equation 4y - 3z = 6:
4y - 3z = 6
-3z = 6
z = -2

Next, let's solve for x in the equation 5x - 3z = 6:
5x - 3z = 6
5x - 3(-2) = 6
5x + 6 = 6
5x = 0
x = 0

So, one point on the plane is (0, 0, -2).

Now, let's solve for x in the equation 5x - 3z = 6:
5x - 3z = 6
5x - 3(-1) = 6
5x + 3 = 6
5x = 3
x = 3/5 or 0.6

Therefore, another point on the plane is (0.6, 0, -1).

In summary, two points on the plane with equation 5x + 4y - 3z = 6 are (0, 0, -2) and (0.6, 0, -1).