Question

someone please help me solve this step by step
3x+y=15
4x+5y=9

Answer 1

By graphing? or algebraically?

Answer 2

by graphing i tried x=0 solve for y but its not right

Answer 3

You have to graph each line separately

Answer 4

the first equation i came up with (4,3)
and did the x=0 solve y for the second

Answer 5

For the first equation:
\[x =0 \implies 3(0) + y = 15 \implies y = 15\]
\[y =0 \implies 3x + 0 = 15 \implies 3x = 15 \implies x = 5\]
This gives the pionts (0,15) and (5,0)
So now you can graph the line that corrisponds to the equation 3x+y=15 by drawing the line between those two points.

Answer 6

Now do the same for the second equation. and see where the two lines cross.

Answer 7

So what do you get for y when you plug in 0 for x in the second equation?

Answer 8

1.8

Answer 9

Just leave it as a fraction for now. It's easier to see =)

Answer 10

9/5 is correct though. Now plug in 0 for y and solve for x.

Answer 11

2.3

Answer 12

Not quite. As I said, leave it as a fraction.

\[y =0 \implies 4x + 5(0) = 9 \implies 4x = 9 \implies x = 9/4 = 2.25\]

Answer 13

9/4

Answer 14

Ok, so what are the two points you have found on this line?

Answer 15

idk im confused, i hate this stuff

Answer 16

(0,1.8) (2.3,0)

Answer 17

Yes, exactly right!

Answer 18

except you keep rounding 2.25 to 2.3 for some reason.

Answer 19

thought i was suppose to

Answer 20

So if you draw a line between those two points it'll give you the line that corresponds to the second equation.

Answer 21

That's fine

Answer 22

I think 2 and 1/4 is easier to graph than 2 and 3/10'ths but it depends on your graph paper I suppose.

Answer 23

Now you're wanting to find where these two lines intersect.

Answer 24

according to my graph they dont

Answer 25

They must. They don't have the same slope, so they are not parallel. Any two distinct non-parallel lines must intersect somewhere.

Answer 26

You will need to continue the line beyond the points that you graphed. It will go straight through those 2 points, but continue on infinitely.

Answer 27

equation 1 i got (0,15) (5,0) drew the line
2nd i got (0,1.8) (2.25,0)

Answer 28

Look real close around the point (6,-3)

Answer 29

i only drew the lines to the points not thru to the end of the graph

Answer 30

You must extend the lines to the point where they intersect. That point is the solution.

Answer 31

ok so then it is considered consistent and dependent

Answer 32

cant figure out how to use my new graphing calc

Answer 33

The each equation by itself has many solutions all points on the line are solutions. But when you consider the two equations together, the point they intersect is the only point that is a solution to both equations.

I am not familiar with term consistent, maybe you can tell me what that term means??

Answer 34

Consistent means that the equations are either the same line (overlapping) or non-parallel. If they are parallel and do not overlap, they are not consistent because there will be no solution. If they are the same line (each one overlaps the other) then they are dependent.

Answer 35

This system is consistent (they aren't parallel) and independent ( they aren't the same line)

Answer 36

Ah so, so you are right tina=ann

Answer 37

yeah thats it, and you can just call me tina

Answer 38

ok

Answer 39

I believe tina uses her calculator and that is why she comes up with decimal answers rather than the exact fraction

Answer 40

tina, I have a graphing calculator, bought it new, still in blister pack at a garage sale for $10.00. I haven't learnt how to use it! lol

Answer 41

yes i use calc, cant figure out how to use my new graphing calc, just spent 150 cant figure out how to use it

Answer 42

your profile says you graduated from Strayer, that is where i am going

Answer 43

I guess you use the book and try and follow their examples, eventually you will learn it.

Answer 44

Mine is the TI-86

Answer 45

Oh really, in VA or DC

Answer 46

ok new problem solve by substitution
6x-2y=-56
5x+48=y

Answer 47

chesapeke Va

Answer 48

mine is TI-Nspire

Answer 49

I went to the Manassas,VA campus, graduated at the Kennedy Center in DC..Ok lets look at the substitution problem. I think we should write the last equation like;
y=5x+48 do you agree?

Answer 50

i think so
i got (-40,-192) for the solution

Answer 51

Humor me as I wade through this, you are ahead of me! lol
I want to subsitute for y in the first equation so it will look like this:
6x -2(5x+48)=-56
6x-10x-96=-56
-4x=40
x=-10

Did I do that right?

Answer 52

yes you did i must of had a brain fart because i forgot to divide

Answer 53

I don't think I violated any laws of algebra!
Now going back to the second equation where we had y=5x+48
substitute are newly found value of x in that we get:

y=5(-10)+48=-2
y=-2

The solution according to the above : x=-10, y=-2

Answer 54

and then you add 60+48 to get 108 right?

Answer 55

oh yeah im way off

Answer 56

is that 10 or -10

Answer 57

It is a -50 added to 48.

Please go over what I did and question me on any thing I did.

Answer 58

im just relearning this and i wasnt ever good at it to begin with

Answer 59

You question the solution of -10 for x?

Answer 60

I will put it here so you can ask away.
I want to subsitute for y in the first equation
so it will look like this: 6x -2(5x+48)=-56 6x-10x-96=-56 -4x=40 x=-10

Answer 61

It didn't paste so well lol should be a new line after the -56
Note that the (5x+48) was substituted for y inthe first equation. Do you see that?

Answer 62

However, in the first equation the coefficient of y was a -2 So you have to multiply (5x+48) by -2 It then becomes -10x-96

Answer 63

ok i got it
i new a new one for you
two angles are supplementary one angle is 3 degrees less than twice the other.
find the measures of the angles

Answer 64

So now the first equation with the substitution of y looks like this:
6x-10x-96=-56 Combining similar terms it becomes:
-4x-96=-56
and so on.

Answer 65

Two angles are supplementary if their sum is what? Is it 90 or 180 degrees?

Answer 66

180 complementary is 90

Answer 67

Let x = one of the angles this then means that 180-x is the other angle. Does seem sensible?

Answer 68

i was taught
x+y=180
x=2y-3
(2y-3)+y=180
3y-3=180
3y=180
y=61
x=2(61)-3
x=119
is this right?

Answer 69

I am looking at your work

Answer 70

You did good until you got to 3y-3=180 good so far. Now look at that step after that and find your error

Answer 71

Did you find your error in that next step

Answer 72

i added 3 instead of subtracting?

Answer 73

Well you should of added 3 to both sides and then you would of had
3y=183

Answer 74

i did and 3y=183
3(61)=183

Answer 75

so y=61

Answer 76

I just saw where you had 3y=180 some how you got the right answer lol

Answer 77

The other angle is supplementary so subtract the 61 from 180 and it is solved!

Answer 78

i wrote it down right on my paper
i got lots of math problems. i just need someone to help me solve them or keep it on track so i get the right answers

Answer 79

Did you say that you have graduated from Strayer or that you are presently going.

Answer 80

presently going

Answer 81

I graduated around 1992. I no longer live in VA or work in DC, I am retired and live in the Ozarks of MO. Way out in the woods! lol

Answer 82

Good luck tina

Answer 83

thank you, im not good at this kind of math