Question

Medal for best answer!!!!!

Given the system of equations presented here:

4x + y = 4


2x + 7y = 28

Which of the following actions creates an equivalent system such that, when combined with the other equation, one of the variables is eliminated?


Multiply the second equation by −1 to get −2x − 7y = −28

Multiply the second equation by −4 to get −8x − 28y = −112

Multiply the first equation by −7 to get −28x − 7y = −28

Multiply the first equation by −2 to get −8x − 2y = −8

Answer 1

@whpalmer4 can u help me?

Answer 2

Does anybody know this?

Answer 3

you want to multiply one of the equations by some constant value, so that when you add them together, one variable will add to zero

Answer 4

Multiply by -2?

Answer 5

notice if you multiply the second by (-2), you get

4x + y = 4
-4x -14 y = -56
-----------------

Answer 6

then when you add the two equations, the x term will drop out (-4 + 4) = 0x

Answer 7

you see that

Answer 8

Yes I do so the right answer is D?

Answer 9

no, that example i just did multiplied the second by -2

Answer 10

Okay but how do I find the answer?

Answer 11

so, instead, how would you make the Y term drop out

Answer 12

Multiply by -1?

Answer 13

try -7 times the first equation

(-7)(4x + y = 4 )

2x + 7y = 28

Answer 14

gives

-28x - 7y = -28
2x + 7y = 28
------------------

Answer 15

adding equation 1 to equation 2 now, the y term goes to zero

-26x + 0y = 0

Answer 16

so -26x = 0

x=0


plug into either to get the y

Answer 17

x=0 , y=4


to solve systems of linear eqn you can -
muyltiply equations by constants
add equations together
switch order of equations

Answer 18

I ended up with 43=28 when plugged into the 2nd equation I don't know If I done it wrong.

Answer 19

I dont know what I am doing that I dont get the answer

Answer 20

start system

4x + y = 4
2x + 7y = 28
---------------


multiply first equation through by -7 to get

-28x - 7 y = -28
2x + 7y = 28
-------------------

Answer 21

So I plug -7 to each of those equations the positive and the negative one?

Answer 22

adding the equations together eliminates y, what the instructions say to do

-28x + 2x - 7y + 7y = -28 + 28

-26x =0

Answer 23

no, multiply each term in the first equation by a -7

Answer 24

Okay so the answer is 3?

Answer 25

multiply first equation through by -7 to get , second equation is not changed

-28x - 7 y = -28
2x + 7y = 28
-------------------

Answer 26

Yes so the 3rd choice

Answer 27

th epoint of that was to eliminate the y variable when you add the two equations together

Answer 28

-26x = 0

Answer 29

so x=0

Answer 30

and if you want to find y, plug x=0 into either of the equations

Answer 31

4x + y = 4
2x + 7y = 28

Answer 32

y = 4, should be the same in both , or you messed up

Answer 33

Yes I got that so 4=4

Answer 34

x = 0, so

4(0) + y = 4 ----->y = 4
2(0) + 7y = 28 -----7y = 28 ---->y = 4

same y=4 from both equations when x=0

Answer 35

Okay I dont get whats the answer should be

Answer 36

another answer they dont include, was what i did at the very start, i figured y first, multiplied second equation by -2, so when added the x term goes away

Answer 37

So which option should I pick then?

Answer 38

The third one, we multiplied the fisrt by -7 to get that


Which of the following actions creates an equivalent system such that, when combined with the other equation, one of the variables is eliminated?
-when combined means when you add them together, one variable will go to zero, like the -7y + 7y = 0y , y is eliminated

Answer 39

Okay can you help me with one more question?

Answer 40

just takes a few practice probs to get it down,

Answer 41

sure i can do one more

Answer 42

Determine the solution to f(x) = g(x) using the following system of equations

f(x) = 5.5x − 13


g(x) = −5x + 18.5


x = 1

x = 2

x = 3

x = 4

Answer 43

I remember doing this but cant remember how

Answer 44

both f(x) and g(x) are functions on the XY plane.

when f(x) = g(x), the two functions intersect at the same point (x,y)

Answer 45

Can u show me how to solve it?

Answer 46

set them equal

f(x) = g(x)

5.5x - 13 = -5x + 18.5

Answer 47

Then?

Answer 48

add 5x to both sides

Answer 49

like this
5.5x - 13 - -5x +18.5
5x 5x

Answer 50

10.5x - 13 = 18.5

add 13 both sides

10.5x = 31.5

Answer 51

divide both sides by 10.5

1x = 31.5 / 10.5

Answer 52

Okay then divide by 10.5

Answer 53

x = 3

Answer 54

yep, the goal is to isolate x by itself

Answer 55

Okay thank you very much for the help!

Answer 56

no prob, anytime