Question

system of equations is shown below:

8x + 5y = 9
3x + 2y = 4

Part A: Create an equivalent system of equations by replacing one equation with the sum of that equation and a multiple of the other. Show the steps to do this. (6 points)

Part B: Show that the equivalent system has the same solution as the original system of equations. (4 points)

Answer 1

FAN AND MEDAL?!

Answer 2

@ranga

Answer 3

lol hey yea sry i was on another window

Answer 4

oh its okay! can you help me?

Answer 5

yep, for the sum of the two equations, just add the left side of the first equation with that of the second, same thing with the right side

Answer 6

well i already solved the first equation and got (1,-1). was i wrong to solve it?

Answer 7

you want me to set them both equal to eachother?

Answer 8

umm no not yet.

Answer 9

okay so what do i do

Answer 10

how did u solve the first equation? when u plug in (1,-1), it doesn't work

Answer 11

i multiplied the first equation (8x+2y=9) by negative one so i could cancel out the Y's. then i just solved using elimination for x then got an x value of 1 and plugged it back into the first equation to solve for y

Answer 12

the Y's wont cancel out, when u multiple +2y by -1, u get -2y, this won't cancel out the +5y from the second equation

Answer 13

oh the first equation is 8x + 5y = 9 not 8x+2y=9

Answer 14

oh wow... i copied down a 2. my bad .!!

Answer 15

so do you want me to solve the two equations first?

Answer 16

its ok, umm...yea, tell me wut u get

Answer 17

okay

Answer 18

so now that there isnt 2s how can i solve them?

Answer 19

??

Answer 20

u can multiply the first equation by 2, and the second equation by 5, this is to get the LCD (least common denominator), ull then get +10y for both equation. now all u hafta do is multiple one of the equation by -1, and the -10y will cancel out the 10y, u can then solve the now-isolated x

Answer 21

u can do the same LCD method for x, and isolate then solve for y

Answer 22

okay hold on

Answer 23

for x i got -2

Answer 24

for y i got 5

Answer 25

yes there we go, correct!

Answer 26

okay cool! so now what do we do to find the equivalent equations? thats the most confusing part

Answer 27

hmm what do you mean equivalent equations? like how 2y = 3 is the same thing as 4y = 6?

Answer 28

yeah. like back up at the problem it says Create an equivalent system of equations by replacing one equation with the sum of that equation and a multiple of the other. Show the steps to do this. (6 points)

Answer 29

hello?

Answer 30

yea im here so sry man :P monitoring the chat...

Answer 31

its okay haha. so what do i do

Answer 32

okay, so they want us to combine the first equation with a multiple of the second equation

Answer 33

how dod i do that? mutliply the second equation by 2 and add it to the first one? wouldnt that only give us one equation?

Answer 34

well, u replace the first equation, the second equation u keep

Answer 35

okay so what dod i multiply the second equation by?

Answer 36

i guess any constant should do

Answer 37

so 2?

Answer 38

lol but i dont get the point thou...this question is weirdly phrased

Answer 39

and i would have 6x+4y=8

Answer 40

and i just add that to the first equation?

Answer 41

lol i guess so yes

Answer 42

so the new first equation i got is 14x+9y=17

Answer 43

u multiplied the second equation by 2?

Answer 44

yes

Answer 45

mmk, that's it?

Answer 46

would my new equivalent equations be 14x+9y=17 and 3x+2y=4

Answer 47

well after i multiplied the second equation by 2 i added it to the first equation

Answer 48

hmm is this homework or like a quiz/test?

Answer 49

its a study guide for a test

Answer 50

but i need the right answer

Answer 51

ah i see

Answer 52

okay so ???

Answer 53

is that new set of equivalent equations right?

Answer 54

OHHH okay so according to Mathwords, an equivalent system of equations is basically another set of equations with the same solution (a point), which, in this case, is (-2, 5)

Answer 55

okay so is my new system i just got not correct?

Answer 56

testing it

Answer 57

okay

Answer 58

yyes it works, oh wow this is such an inconvenient way to do this lol never seen anything like this

Answer 59

i KNOW! very complicated! thank you so much. can you help me do another?

Answer 60

yea of course

Answer 61

okay hold on im going to attach the file so itll be easier to see

Answer 62

mmk

Answer 63

/Users/lyndsay/Desktop/Screen Shot 2014-05-23 at 11.54.37 PM.png

Answer 64

ugh sorry trying to figure out how to attch it

Answer 65

LOL yea

Answer 66

Can you open it?

Answer 67

yes

Answer 68

okay

Answer 69

well for part a, ur basically just substituting the two original functions, this is an example of an equivalent system of equations, and as we're already talked about, they will have the same solution(s)

Answer 70

so i substitute what? The question itself is worded weird

Answer 71

ur substiuting the 2 y's in the second equation

Answer 72

y = y, replaced y's, u get the second equation, get it? sry i cant explain this smoothly lol

Answer 73

so for part A the answer would be because they are both equivalent equations?

Answer 74

yea, don't forget to mention the word "sustitute"

Answer 75

so i should write They are both equivalent equations because they are substituted into the equation? or how should i word it?

Answer 76

They have the same solutions because they are an example of an equivalent equation system, having been substituted by the previous 2 y equations

Answer 77

okay so now for part b?

Answer 78

u know how 4 is 2 ^ 2? and so 4^x can be rewritten as 2 ^2x, do u understand this rule?

Answer 79

yes

Answer 80

ok, so u also know that if 2 exponential functions have the same root, their powers are equal, yes?

Answer 81

yes then you can set the exponents equal and solve for x right?

Answer 82

yes, but remember to turn the base 4 into base 2

Answer 83

okay. so how do i do the table of values?

Answer 84

or wait what does it mean by make tables??

Answer 85

yes, so just plug in x values that are within the given range

Answer 86

okay so the equation would be 2^2x=2^x+3??

Answer 87

then i just make a table to plug in values?

Answer 88

yes, so set 2x equal to x + 3

Answer 89

x=3

Answer 90

lol wth...

Answer 91

what?

Answer 92

i set 2x=x+3 and solved for x

Answer 93

lol yea i know and ur correct, just the table part...

Answer 94

im confused on how to plug in the values

Answer 95

like idk how i should make the table nd what to plug in where

Answer 96

oh maybe u weren't suppose to solve it via base-changing, but plug and chug..plug in x for values between -3 and 3, and use the coordinates to make the table. when the 2 equation equals, there's ur solution (although we found it already lol derp)