Question

PLEASE HELP ME!!!!!?
Determine which system below will produce infinitely many solutions.

-6x + 3y = 18
4x - 3y = 6

2x + 4y = 24
6x + 12y = 36

3x - y = 14
-9x + 3y = -42

5x + 2y = 13
-x + 4y = -6

Answer 1

An equation have infinitely many solution when it have the same slope and y-intercept can u change the equations to slope-intercept form?
And WELCOME TO OS :D

Answer 2

ummmm....... I'm not good at doing that. @Godlovesme

Answer 3

I wish I could write it all for u but I have gtg I'll tag someone that could help u sorry @jim-thompso

Answer 4

thank you! @Godlovesme

Answer 5

hi everyone I am new here I need help

Answer 6

NP :)I really really apologize =0

Answer 7

can you help me @Preetha ?
Its ok if I need helpm with something else in the future ill ask @Godlovesme

Answer 8

K I would suggest u to use geogebra which helps u graph and u canc whenu enter the eqns and if oonly one line pops up...BINGO! LOLL xD thanks for the medal too!!

Answer 9

ok thanks! @Godlovesme

Answer 10

Godlovesme has a good suggestion. If you graph a system and you get 1 line showing up, which in reality is a situation where 1 line overlaps another perfectly (covering it up), then you'll have a dependent system with infinitely many solutions.

Answer 11

its not letting me down load it for some reason! @jim_thompson5910

Answer 12

that's ok, there's always desmos

https://www.desmos.com/calculator

it's an online calculator you don't need to download

Answer 13

graph each system one at a time

Answer 14

ok so i know a isnt it. Am i correct so far? @jim_thompson5910

Answer 15

yes choice A should have 2 lines that cross at exactly 1 point

Answer 16

that crossing point, or intersection point, is the only solution

so there aren't infinitely many solutions for choice A

Answer 17

wait is is c then @jim_thompson5910

Answer 18

you are correct

Answer 19

that system should produce 1 line (2 lines really, one hidden below another)

Answer 20

because there is infinitely many solutions for it because both lines are exactly the same!

Answer 21

exactly

Answer 22

thank you for sending that link! that helped a lot!!!!!! :) @jim_thompson5910

Answer 23

I'm glad it did

Answer 24

do you think you can help with one more!? @jim_thompson5910

Answer 25

sure

Answer 26

Solve the system of equations by substitution. What is the solution for x?

2x + y = 1
4x + 2y = -1


a.) x=0
b.) x=2
c.) there is no x value, as there is no solution
d.) x can be any value, as there is infinitely many solutions
@jim_thompson5910

Answer 27

are you able to solve 2x + y = 1 for y?

ie are you able to isolate y in the equation 2x + y = 1 ?

Answer 28

yes you can.

Answer 29

@jim_thompson5910

Answer 30

what do you get when you solve for y

Answer 31

-1

Answer 32

no

Answer 33

subtract 2x from both sides


2x + y = 1

2x + y-2x = 1 -2x

y = -2x + 1

Answer 34

hopefully you see how that works?

Answer 35

Yes i did it differently i forgot that way

Answer 36

now you focus on the second equation and replace y with -2x+1

4x + 2y = -1

4x + 2(-2x+1) = -1 ... replace y with -2x+1

solve for x

Answer 37

ok so there is no solution. am i correct? therefore the answer is c.

Answer 38

@jim_thompson5910

Answer 39

correct, you should have 2 = -1 when you simplify

Answer 40

yep thats what i got!!!!!!!!!!!!!!! thank you sooooo much you made this clear to me

Answer 41

you're welcome