Question

Can someone explain this to me? Will medal.

A 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.

Answer 1

@Nnesha @SolomonZelman

Answer 2

still need help? :)

Answer 3

yes!

Answer 4

I would do elimination.

Answer 5

hey @bloofoffiction do u know how to use the substitution method?

Answer 6

I think so

Answer 7

\(\large\color{blue}{8x + 5y = 9 \\ 3x + 2y = 4}\)

\(\large\color{blue}{16x + 10y = 18 \\ -15x -10y = -20}\)

Answer 8

I multiplied first equation times 2, and the second times -5. Can you add the equations now?

Answer 9

yes

Answer 10

so what do you get, after adding?

Answer 11

u can do that too

Answer 12

x+x=18 ?

Answer 13

or 2x=18

Answer 14

well, this is what we are trying to do,

\(\large\color{black}{\color{red}{16x} ~~~~~~~~~\color{green}{+ 10y }~~~~=~~~~~~~\color{blue}{ 18} \\\color{red}{-15x}~~~~~\color{green}{- 10y } ~~~~= ~~~~\color{blue}{ -20} }\)

Answer 15

We are adding/subtracting everything separately.
1) the Axes.
2) the whYs.
3) the Constants. (on the right hand side of each equation).

Answer 16

ok

Answer 17

so what do you get?

Answer 18

x=-2 ?

Answer 19

I'm terrible at algebra

Answer 20

Yes, there you. And the whYs, cancels, as you already figured;)

Answer 21

I meant there you go.

Answer 22

\(\large\color{black}{\color{red}{16x} ~~~~~~~~~\color{green}{+ 10y }~~~~=~~~~~~~\color{blue}{ 18} \\\color{red}{-15x}~~~~~\color{green}{- 10y } ~~~~= ~~~~\color{blue}{ -20} }\)

gives as, as you already said, and were correct,

\(\large\color{black}{x=-2 }\)

Answer 23

ok

Answer 24

So, once you found the x, you can plug it back for to find the y, into any of the original equations.

If you plug it into both of the equatins, and find te same result for y, this will then not only solve for x, but also verify that the solution is correct.

Answer 25

reminding, the original equations are:

\(\large\color{black}{\color{red}{8x} ~~~~~\color{green}{+ 5y }~~~~=~~~~\color{blue}{ 9} \\\color{red}{3x}~~~~~\color{green}{+2y } ~~~~= ~~~~\color{blue}{ 4} }\)

Answer 26

\[8(-2)+5y=9\]

Answer 27

\[3(-2)+2y=4\]

Answer 28

yes.

Answer 29

what do you get in each equation?

Answer 30

\[16+5y=9\]

Answer 31

what is that for?

Answer 32

My self mostly

Answer 33

I think I've done something wrong because I got y=-1.4

Answer 34

yes, you got something wrong, lol... let
s fix that:)

Answer 35

I would subtract 16 from 9...

Answer 36

\(\large\color{black}{ 8(-2) + 5y = 9 \\ 3(-2) + 2y = 4 }\)


\(\large\color{black}{ -16 + 5y = 9 \\ -6 + 2y = 4 }\)

Answer 37

you are adding, because the 16 and the 6 are negative. right?

Answer 38

oops my bad

Answer 39

so y = 5 ?

Answer 40

yes.

Answer 41

and the equivalent systems would be \[16x+10y=18\] and \[-15x-10y=-20\] ?

Answer 42

the first equation si riht, let me check the other one.

Answer 43

yes, and the second one is correct as well.

Answer 44

ok. Thank you so much! You're the best.

Answer 45

You can use my thing for this.
`\(\large\color{black}{ 8x + 5y = 9 \\3x + 2y = 4 }\)`

try to copy paste what is in gray, please.

Answer 46

\(\large\color{black}{ 8x + 5y = 9 \\3x + 2y = 4 }\)

Answer 47

can I ask a quick question?

Answer 48

yes.

Answer 49

Why did you multiply the second equation by -5 not positive 5. I need to show the steps and I would like to be able to explain it.

Answer 50

I could have multiplied times 5 and subtracted the equations, but then you confuse is it like
\(\large\color{black}{ a-b }\) or \(\large\color{black}{ b-a }\),
but in when we are adding, it would matter which way we are going,
\(\large\color{black}{ a+(-b) }\) or \(\large\color{black}{ (-b)+a }\)

Answer 51

I mean it wouldn't matter, for the last hrase.

Answer 52

ok thanks

Answer 53

Anytime;)

Answer 54

Also, if you want to type the \ symbol.

1) Click and hold ALT.
2) Click 2 9 on the number pad on the left corner of the keyboard.
3) Release the ALT key.

you get, \ .

Answer 55

So if you are typing in a parenthesis latex, ` \(\large\color{black}{ }\) ` you can do it without copy pasting.

Answer 56

ok I'll keep that in mind

Answer 57

`\(\large\color{black}{ }\)` this gives you an advantage of typing inside the text, like

" \(\large\color{black}{ a+(-b) }\) is the same thing as \(\large\color{black}{ (-b) +a }\)."

Answer 58

yes, don't want to be too annoying... you welcome, once again:)