Question

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)

Answer 1

do you know how to plot graphs?

Answer 2

I need feedback to help you.

Answer 3

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

Answer 4

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.

Answer 5

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.

Answer 6

you said the x and y both represent the independent.

Answer 7

sorry, y represents the dependent variable.

Answer 8

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.

Answer 9

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

Answer 10

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

Answer 11

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

Answer 12

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

Answer 13

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)

Answer 14

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

Answer 15

Okay.

Answer 16

5y?

Answer 17

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

Answer 18

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

Answer 19

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

Answer 20

so express bonus in english, or in an equation.

Answer 21

are you getting what I am saying?

Answer 22

ah not really

Answer 23

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

Answer 24

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

Answer 25

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

Answer 26

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

Answer 27

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

Answer 28

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

Answer 29

so how did I do?

Answer 30

okay thats great!

Answer 31

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

Answer 32

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

Answer 33

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.

Answer 34

y is value/5.

Answer 35

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.

Answer 36

so one value could be (5,4)

Answer 37

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

Answer 38

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

Answer 39

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

Answer 40

sorry fiured wrong. redid it and got 4.

Answer 41

okay, next choose x =10

Answer 42

ok I got 11

Answer 43

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.

Answer 44

right

Answer 45

so what is the second equation?

Answer 46

7x=5y+15

Answer 47

this is the same equation as before.

Answer 48

the other one was 7x-5y=15

Answer 49

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

Answer 50

y=-7x+15

Answer 51

what?

Answer 52

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