Question

A system of equations is shown below:

-3x + 7y = -16
-9x + 5y = 16

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

Part A: equation (1) -3x + 7y = -16
equation (2)-9x + 5y = 16

replace (2) by adding (2) to two times (1):
2 times (1): -6x + 14y = -32
Add (2): -9x + 5y = 16
--------------------
-15x + 19y = -16

So the second pair of equations are:
-3x + 7y = -16 (1)
-15x + 19y = -16 (3)

Answer 2

I just need help with Part B

Answer 3

@undeadknight26 @itsbribro

Answer 4

i think it would be solve for 1 and 2 x,y
And then solve for 1 and 3 x,y

Answer 5

@KlOwNlOvE i need you help

Answer 6

@Catlover5925 @dtuniyants @dan815

Answer 7

@perl

Answer 8

I'm not a dude -.-

Answer 9

okay sorry will you please help me tho.

Answer 10

And I have no idea how to do this, sorry

Answer 11

no hold on

Answer 12

i just need help finding x and y for -3x+y=-16
-9x+5y=16
-15x+19x=-16

Answer 13

-3x+7y=-16

Answer 14

@perl

Answer 15

it would be easier if you redid part a)

Answer 16

why was it wrong?

Answer 17

but if you will help me through it i will.

Answer 18

its not wrong, but you didn't solve for x and y

Answer 19

okay so we will restart where do you want to start?

Answer 20

actually lets keep your original work

Answer 21

brb

Answer 22

okay

Answer 23

so we want to show that the 'new system of equations' has the same solution as the 'old system of equations'

Answer 24

yes

Answer 25

to show that, lets plug in the solution into both system

Answer 26

first can you make sure my part A is correct?

Answer 27

ok

Answer 28

i had to reboot my computer , this website is super glitchy

Answer 29

yeah okay so can you check then go to part B?

Answer 30

part b)
show that system :
-3x + 7y = -16
-9x + 5y = 16

has same solution as system :
-3x + 7y = -16
-15x + 19y = -16

Answer 31

yes

Answer 32

ok plug in x = -4, y = -4
(that is the solution for the first system )

Answer 33

so where do i plug it in?

Answer 34

for x and y

Answer 35

for all 4 of them?

Answer 36

12+(-28)
36+(-20)
60+(-76)

Answer 37

@perl

Answer 38

is that right? i checked and it was

Answer 39

part b)
show that system :
-3x + 7y = -16
-9x + 5y = 16


has same solution as system :
-3x + 7y = -16
-15x + 19y = -16


Plug in (x,y) = (-4,-4)

system 1:

-3(-4) + 7(-4) = 12 - 28= -16
-9(-4) + 5(-4) = 36 - 20 = 16

system 2:

-3(-4) + 7(-4) = 12-28 = -16
-15(-4) + 19(-4) = 60 -76= -16


so (-4,-4) is the solution for both systems.
therefore the systems of equations are equivalent

Answer 40

Thanks so much