Hi all. I have 4 problems that I am having a very hard time with so need some help please. Solve the system of equations by graphing: 7x-5y=15 & 7x=5y+15. Need solution set (ordered pair)

- anonymous

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- anonymous

do you know how to plot graphs?

- anonymous

I need feedback to help you.

- anonymous

sorry had to step away. I have a hard time with graphing.

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- anonymous

okay. graphs have a dependent variable and an independent variable. The x axis represents the independent variable and the y axis represents the independent variable.

- anonymous

so, now choose any values of x for your equation 7x - 5y = 15. That is, choose any values of x and you will get a corresponding dependent value of y.

- anonymous

you said the x and y both represent the independent.

- anonymous

sorry, y represents the dependent variable.

- anonymous

let me give you an example. suppose you are a salesman. Your year end bonus is 10% of sales you make that year. So, the sales you make is an independent variable. You can make 10000 dollars worth of sales, or if you are better than average, you make 20000 dollars of sales. Or if you are brilliant, you make $100,000 of sales. But notice what happens. The bonus is 10% of your sales. So the more sales you make, the more bonus you get. In other words, the bonus is dependent on sales.

- anonymous

unfortunately all dependent variables are not so easily represented as 10% of the independent variables. suppose your bonus was 10% of sales - medicare - 1/2taxes

- anonymous

then your equation would be bonus = sales/10-M-1/2tax

- anonymous

anyway, the point is, there are independent variables which are in your hand.

- anonymous

and there are other variables which depend on your independent variable.

- anonymous

so in your equation, 7x - 5y = 15, let say x is the independent variable, just because it is nice to have the x variable on the independent axis (x-axis)

- anonymous

so then, what is the dependent variable, in terms of x?

- anonymous

Okay.

- anonymous

5y?

- anonymous

if bonus is 10% of sales, express bonus in terms of sales. similarly if 7x-5y is 15, express y in terms of x.

- anonymous

basically, you are trying to express the dependent variable as a function of the independent variable.

- anonymous

you could say that 7x-5y = 15 is " 7 times your sales minus 5 times your bonus always gives 15 grand"

- anonymous

so express bonus in english, or in an equation.

- anonymous

are you getting what I am saying?

- anonymous

ah not really

- anonymous

sorry that is one area I just seem can' get a grasp on

- anonymous

okay if 7 times sales minus 5 times bonus is always 15 grand, then 7 times sales minus 15 grand divided by 5 is the bonus.
in other words, y = (7x-15)/5

- anonymous

so choose your x values and find out the corresponding y values.

- anonymous

since this is the equation for a line, you need only two points.

- anonymous

ok so here is what I did. tell me if I am rght

- anonymous

I chose 2 for x. y=7(2)-15/5.... y=14-15/5.... y=-1/5

- anonymous

so how did I do?

- anonymous

okay thats great!

- anonymous

but 1/5 is kinda hard to plot on a graph.

- anonymous

yes very true. do I need to choose a different number or x?

- anonymous

notice that y i some value/5. so if the value is a multiple of 5, then you would get a nice round number for y.

- anonymous

y is value/5.

- anonymous

so suppose you chose x = 5. 7 times 5 is 35, and 35-15 is 20. 20 is a multiple of 5. so y =4.

- anonymous

so one value could be (5,4)

- anonymous

ok I changed the value of x to 5. I came up with y= -3

- anonymous

both are nice round numbers, easy to plot on a pice of graph paper.

- anonymous

how did you come up with y = -3 for x = 5?

- anonymous

sorry fiured wrong. redid it and got 4.

- anonymous

okay, next choose x =10

- anonymous

ok I got 11

- anonymous

okay great! so you have two points (5,4) and (10,11). there is only one line which passes through both points. So you have your first line down on the graph! huzzah! one down, one equation to go.

- anonymous

right

- anonymous

so what is the second equation?

- anonymous

7x=5y+15

- anonymous

this is the same equation as before.

- anonymous

the other one was 7x-5y=15

- anonymous

okay, subtract 5y from both sides of your second equation and post what you got.

- anonymous

y=-7x+15

- anonymous

what?

- anonymous

how did you get that?
http://www.dabbleboard.com/draw?b=Guest644716&i=0&c=3327a9e1158d904a38fbad735c24ed28cad7bcd9
show me there.

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