# Math Help - Solve Simultaneous Equations Graphically?

1. ## Solve Simultaneous Equations Graphically?

Hi I have two questions that I need help on.

Solve Graphically

(a) 2x – 3y = 11/12 and x + y = -7/12

(b) y = 30 – 6x + 2x2 and y = 2(x + 11)

Im really not sure how to do this at all and would apppreciate any help. I've never hadany experience before solving simultaneous equations graphically so please if you wouldn't mind be detailed. Thanks

2. ## Hi

Hi

I am not sure what you mean, but if you mean solve a system of linear equations, then you are asking for the intersection between two lines.

For a graphic solution you should plot both lines with your calculator, MATLAB or whatever, and look for the intersection point.

I have to find the values of X and Y for both questions by hand (drawing graphs). I can't really ask my teacher for any help due to the Easter holiday. If its no trouble could anyone possibly draw up these two graph and find the x and y values for both questions and maybe scan the graphs in and send them to my email address (Sailee316@googlemail.com) or if not just tell me how to go about these two questions step by step. Thanks

4. Originally Posted by Sailee316
Hi I have two questions that I need help on.

Solve Graphically

(a) 2x – 3y = 11/12 and x + y = -7/12

(b) y = 30 – 6x + 2x2 and y = 2(x + 11)

Im really not sure how to do this at all and would apppreciate any help. I've never hadany experience before solving simultaneous equations graphically so please if you wouldn't mind be detailed. Thanks
For a), transpose both equations to make y the subject. Then they are easier to graph.

You should get $y = \frac{2}{3}x - \frac{11}{36}$ and $y = -x - \frac{7}{12}$.

Then just graph them and see where the point of intersection lies.

For b) you should just be able to put them into your calculator as given and graph them. See where the point(s) of intersection lie.

5. Originally Posted by Sailee316
...could anyone possibly draw up these two graph and...
They were supposed to have covered graphing before assigning this sort of exercise...

To learn how to graph linear equations, try here.

6. Originally Posted by Prove It
For a), transpose both equations to make y the subject. Then they are easier to graph.

You should get $y = \frac{2}{3}x - \frac{11}{36}$ and $y = -x - \frac{7}{12}$.

Then just graph them and see where the point of intersection lies.

For b) you should just be able to put them into your calculator as given and graph them. See where the point(s) of intersection lie.
Hi. Thanks for your reply. Im still a bit stuck on question a). Im not sure how to find which points to plot. I will need to find the points for question b) aswell so I suppose I will need to learn how to do the points. I dont get how to find points from points from fractions. I would appreciate your help on finding the points. Thanks

7. Originally Posted by Sailee316
Im not sure how to find which points to plot.
Ah; so you haven't read the lesson yet...

Try studying the lesson in the link provided, as it explains the process for finding plot-points. In particular, it explains that the x-values are entirely up to you!

8. Hi. I tried finding the values for Y by choosing the values for X (-6 to 6) and I dont think im doing it exactly right . If I put x= -6 into the equation

I get -4.30555556 which I don't know how to plot. I need some help doing this kind of stuff. I need to get the points for as well. I read through the lesson but I dont get it as the lesson doesn't show how to deal with numbers like -4.30555556 (thats if im actually doing it correctly). So

how do I find the points for
and (which is the first question.

And then plot
y = 30 – 6x + 2x2 and y = 2(x + 11). i dont have a graphing calculator or anything like that so i cant see what it should look like .

Any more help would be appreciated greatly. Thanks

9. Try using the technique explained and demonstrated in the lesson:

If you aren't comfortable using fractions or decimals, then, for y = (1/36)(24x - 11), try to find x-values that will make 24x - 11 a multiple of 36, so the fractions (or decimals) cancel out.

For instance, 24x - 11 = 36 for 24x = 47, so x = 47/24 (or, for graphing, nearly x = 2). When x = 47/24, then 24x - 11 = 36, so y = (1/36)(36) = 1.

And so forth.

10. ## Y = mx + b

Hi. I have this question on my assignment:

2. Solve graphically:

(a) 2x – 3y = 11/12 and x + y = -7/12

(b) y = 30 – 6x + 2x2 and y = 2(x + 11)

Does this mean I have to do 4 seperate graphs or just 2? I did some research and found I need to reaarange and find points to plot but im having trouble rearrainging the four different equations. Thanks

11. ## 2

only 2

12. Originally Posted by Sailee316
2. Solve graphically:

(a) 2x – 3y = 11/12 and x + y = -7/12

(b) y = 30 – 6x + 2x2 and y = 2(x + 11)

Does this mean I have to do 4 seperate graphs or just 2?
For each of the two listed systems of equations, you would do one graph, each graph showing two lines.

13. Not sure whether you know this or not, but on your graphs that you've drawn, the places where the lines intersect are the solutions to the equations

14. Originally Posted by craig
Not sure whether you know this or not, but on your graphs that you've drawn, the places where the lines intersect are the solutions to the equations
Yeah I know that part. Im ok at drawing the graphs but I need help with finding all the points to plot. Thanks

Originally Posted by stapel
Try using the technique explained and demonstrated in the lesson:

If you aren't comfortable using fractions or decimals, then, for y = (1/36)(24x - 11), try to find x-values that will make 24x - 11 a multiple of 36, so the fractions (or decimals) cancel out.

For instance, 24x - 11 = 36 for 24x = 47, so x = 47/24 (or, for graphing, nearly x = 2). When x = 47/24, then 24x - 11 = 36, so y = (1/36)(36) = 1.

And so forth.
Hi. Could you explain in more detail which numbers I have to plot exactly. Is there any kind of calculator (online) for generating points? Thanks

15. Originally Posted by Sailee316
Yeah I know that part. Im ok at drawing the graphs but I need help with finding all the points to plot. Thanks

Hi. Could you explain in more detail which numbers I have to plot exactly. Is there any kind of calculator (online) for generating points? Thanks
Substitute a value of x into the rule, calculate the value of y, plot the point.

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