anonymous 5 years ago I am working on solving the system of equations by graphing. I am having some problems so I hope someone can show me an easier way of doing this. This is what I have x-3y=-3 & x+3y=9.

1. anonymous

solve each equation for one of the two variables you have as: x-3y=-3 will be x=3y-3. (1) x+3y=9 will be x=9-xy (2) find any two points in each function, and connect them with a line. the intersection point is your solution.. I hope that would help

2. anonymous

the second equation is x=9-3y.. sorry for the typo!!

3. anonymous

That is were I am running into problems. I think I am getting the first one. Here is what I have so far. 1st equation: x-3y=-3. I got y=1/3x-3/3(1) x=3 and y=1 2nd equation: x+3y=9. I got y=-1/3x+9/3(3) x=9 and y=3 The problem I am having is figuring out the second point to draw the line.

4. anonymous

Can you show me something that will work on all the equations?

5. anonymous

take any value of x and find the corespondent value of y.. this is a new point

6. anonymous

so just pick any number for x to solvethe equation?

7. anonymous

well is it okay if we work in my equations.. it looks much simpler. you know how I got them anyway?

8. anonymous

so is my work right so far?

9. anonymous

I didn't check it.. let me

10. anonymous

11. anonymous

hmm I don't think you're following the right method.. you're asked to solve them by graphing.. so find any two points in the line and coonnect them. do this to both lines, just find where they intersect and you're done.

12. anonymous

to get points.. just substitute any value for x, get the corespondent value of y.. this is a point

13. anonymous

Ok but I never worked i you way. They are showing us theway I put I wrote it. So now I am kind of confused.

14. anonymous

should be worked it your way.

15. anonymous

watch this.. it may help

16. anonymous

I will do your problem the way that's usually done by steps: 1) solve both equations for y: 1st equation: $y={1 \over 3}x+1\rightarrow (1)$ 2nd equation: $y={-1 \over 3}x+3 \rightarrow(2)$

17. anonymous

18. anonymous

2) find two points for each equation (intersection points are usually preferred): 1st for equation (1): $x=0 \implies y=1, x=3 \implies y=2$ so we have the two points in the first line which are (0,1) and (3,2)

19. anonymous

for equation (2): $x=0 \implies y=3, x=3 \implies y=2$ we have two points in the second line, which are (0,3) and (3,2)

20. anonymous

3) draw the line of each equation by connecting the two pints in each one

21. anonymous

4) find the point they intersect at (x,y), this point is the solution of the linear system!! :)

22. anonymous

I guess that was confusing to you, but you should have said thanks :P

23. anonymous

sorry had to go help the wife fix supper. Will look it over closely and use to try my next problem and see if I get it right. Thank you very much for your help.