# Thread: graphing

1. ## graphing

Hi;
How do I graph x + y + z = 6.

Thanks.

2. ## Re: graphing

Originally Posted by anthonye
Hi;
How do I graph x + y + z = 6.

Thanks.
This equation defines a plane. If you have been given this question, you should have been taught about planes. What have you tried, where are you stuck?

3. ## Re: graphing

stuck at the beginning I do maths just as a hobby I understand it can be graphed
but don't know how .

thanks

4. ## Re: graphing

Originally Posted by anthonye
Hi;
How do I graph x + y + z = 6.

Thanks.

x=0, y=0 ==> z=6
x=0, z=0 ==> y=6
y=0, z=0 ==> x=6

So, (0,0,6), (0,6,0) and (6,0,0) are points on your plane, draw them on 3D, could you see your plane now?

5. ## Re: graphing

Ok got it thanks any websites on this stuff that you know of.

6. ## Re: graphing

What I'm trying todo is graph this system of equations,
x + y +z =6
x - y + z =2
x + 2y - z = 2

But I can't find thire solution how do you do that?

7. ## Re: graphing

Originally Posted by anthonye
What I'm trying todo is graph this system of equations,
x + y +z =6
x - y + z =2
x + 2y - z = 2

But I can't find thire solution how do you do that?
add the first two equations term for term ...

2x + 2z = 8

x + z = 4

substitute 4 in for (x + z) in the second equation ...

4 - y = 2

y = 2

add the second and third equations ...

2x + y = 4

sub in 2 for y ...

2x + 2 = 4

x = 1

sub x = 1 and y = 2 into the first equation ...

1 + 2 + z = 6

z = 3

8. ## Re: graphing

Originally Posted by anthonye
What I'm trying todo is graph this system of equations,
x + y +z =6
x - y + z =2
x + 2y - z = 2

[snip]
Why?

9. ## Re: graphing

Just interested I want to know how to graph them and find their solution
graphically.

Thanks.

10. ## Re: graphing

Skeeter went to a great deal of work to show that the three planes intersect at the single point (1, 2, 3) but apparently you did not ask that.

You have already been shown how to determine that x + y +z =6 is the unique plane containing the points (6, 0, 0), (0, 6, 0), and (0, 0, 6).

x - y + z =2

If x= y= 0, z= 2. If x= z= 0, -y= 2, y= -2. If y= z= 0, x= 2.
x- y+ z= 2 is the unique plane containing the points (0, 0, 2), (0, -2, 0), and (2, 0, 0).

x + 2y - z = 2

if x= y= 0, -z= 2 so z=-2. If x= z= 0, 2y= 2 so y= 1. If y= z= 0, x= 2.
x+ 2y- z= 2 is the unique plane containing the points (0, 0, -2), (0, 1, 0), and (2, 0, 0).

11. ## Re: graphing

Yes I know and I always thank you all for your help but I need to see how this is done graphically.

Just for the fact I whould of learnt something else mathmatically.

12. ## Re: graphing

Originally Posted by anthonye
Yes I know and I always thank you all for your help but I need to see how this is done graphically.

Just for the fact I whould of learnt something else mathmatically.
You have been shown how to draw the plane x + y +z = 6 and you have been shown how to solve the equations algebraically. I suggest you use a Computer Algebra System to draw all three equations. You will see three planes, and all three intersect at a single point, viz. (1, 2, 3).

I don't see that any more can be said, particularly since you "do maths just as a hobby" and hence your exposure to and understanding of the pre-requisite mathematical concepts is an unknown quantity.

13. ## Re: graphing

Ok I can draw these graphs I just can't find the point of intersection I need to be shown this graphically please.

Can someone show me this on a graph?

Thank you.

14. ## Re: graphing

Anyone know where I can get help on this matter?

Thanks.

15. ## Re: graphing

Originally Posted by anthonye
Anyone know where I can get help on this matter?

Thanks.
As I have already said, use a Computer Algebra System.

Thread closed.