Question

Determine which system below will produce infinitely many solutions.

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

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

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

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

i really need help

@jigglypuff2

Answer 1

@Hero

Answer 2

i think its C

Answer 3

@SkiTTleoooo47 can you help me please??

Answer 4

@jim_thompson5910 will you help me please?

Answer 5

is C a random guess or do you have something to back you up on why you think it's C?

Answer 6

a random guess I'm not good at this at all can you please teach me?

Answer 7

one good way to go about this is to graph each system

Answer 8

I'd use

https://www.desmos.com/calculator

if you don't have a graphing calculator

Answer 9

how does it let you know how many solutions it can produce?

Answer 10

each equation generates a line, so you'll have 2 lines (2 equations ---> 2 lines)

where the two lines cross is where the solution is

Answer 11

if you get 2 parallel lines, then there are NO solutions

if you have one line lie completely and perfectly on top of the other, then you get infinitely many solutions

Answer 12

how many times it crosses with each other will let you know how many solutions there are right?

Answer 13

correct, with a system of linear equations, there are only these scenarios


A) exactly one solution (one intersection point)

B) NO solutions at all (with parallel lines never crossing)

C) infinitely many solutions (one line lies completely and perfectly on top of the other)

Answer 14

oh ok but don't i have to y=mx+b? or something to get a slope

Answer 15

you can convert each equation into slope intercept form

but luckily the graphing calculator I posted above lets you type in any equation of any form (and it will graph it)

Answer 16

oh really? so it'll graph it and then what do i do?

Answer 17

A is no solution so it can't be that right?

Answer 18

here's what we get when we graph the system in choice A

notice the colors:
the red line is the first graph -6x+3y=18
the blue line is the second graph 4x-3y=6

Answer 19

In the image of the graph, we see that the two lines are NOT parallel

so they cross somewhere

they cross at (-12,-18) which is the solution to the system of equations

this is the only solution to this system of equations

Answer 20

oh ok i did that one wrong I'm still trying to get the hang of this calculator but B is no solution

Answer 21

Is A the answer?

Answer 22

look back at the instructions "Determine which system below will produce infinitely many solutions."

Answer 23

ok so A produces one and B does not so far right?

Answer 24

correct, A has one solution B has none

Answer 25

so neither are the answer

Answer 26

it's either C or D

Answer 27

For c i got 2 solutions?

Answer 28

how did you get 2 solutions?

Answer 29

it had 2 points on the line.

Answer 30

it only had 1 line and 2 points on it

Answer 31

did you graph both equations?

Answer 32

yes i think its D is that correct?

Answer 33

how many solutions does D have?

Answer 34

3? and oh yeah i graphed C wrong i put only one equation sorry

Answer 35

with a system of linear equations, there are only these scenarios


A) exactly one solution (one intersection point)

B) NO solutions at all (with parallel lines never crossing)

C) infinitely many solutions (one line lies completely and perfectly on top of the other)

Answer 36

on C and D I'm confused

Answer 37

can you post a screenshot of what you got when you graphed system D

Answer 38

I want to see what you're getting

Answer 39

ill try

Answer 40

this is what i got?

Answer 41

ok I see now, thanks

notice how the two lines (the purple and orange) cross at exactly one point

so there is exactly one solution

Answer 42

by the way, I recommend zooming in to better see the solution point

Answer 43

so that rules out choice D since D has exactly one solution

Answer 44

Ok there were three points like ordered pairs when i zoomed in on one what does that mean?

Answer 45

3 points?

Answer 46

yes

Answer 47

oh those other two points you're able to click on are the x-intercept and y-intercept

Answer 48

these points (x-intercept and y-intercept) are where the line crosses the x and y axis

Answer 49

what we care about is where the two lines cross (ignore the axis)

Answer 50

ok should i show you what i got for c?

Answer 51

sure go for it

Answer 52

oh wait its C right? because i typed in both equations and it overlapped completely

Answer 53

correct, you can turn one equation on and off to see it blinking on top of the other

Answer 54

the perfect match means there are infinitely many intersections ----> infinitely many solutions

Answer 55

ok I'm new on this site so thank you soo zoo much for your help and taking your time to help me! :)

Answer 56

soo*

Answer 57

you're welcome and welcome to the OpenStudy

Answer 58

thanks

Answer 59

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