Question

1) Start by creating a Non-Linear system of equations. This means that at least one of your equations must have an exponent
2) Solve your system by graphing. Make sure that you detail the steps you took and include an image of the graph.
3) Solve your system algebraically (Elimination or Substitution). Make sure that you detail the steps and show your work.
4) Give your opinion of which method is best.

Answer 1

@jim_thompson5910 could you help?

Answer 2

@sammixboo

Answer 3

@TheSmartOne

Answer 4

how far did you get?

Answer 5

i think i have an 2 equations i want to use @jim_thompson5910

Answer 6

what equations

Answer 7

x^2+8=y and 3x^2=y

Answer 8

@jim_thompson5910

Answer 9

so that answers this question: 1) Start by creating a Non-Linear system of equations. This means that at least one of your equations must have an exponent

Answer 10

2) Solve your system by graphing. Make sure that you detail the steps you took and include an image of the graph.

so you need to graph now

Answer 11

its has to be online so could i use geogebra? @jim_thompson5910

Answer 12

geogebra is a good choice as that's the graphing tool I use (it's a very cool program)

Answer 13

confusing for a first time user lol o_O @jim_thompson5910

Answer 14

this is the graph i have now @jim_thompson5910

Answer 15

That's true. It's a bit tricky, but once you get the hang of it, it's not too bad.

Answer 16

ok you can use the point tool to find the intersection of the two curves

Answer 17

that effectively solves the system graphically

Answer 18

i was leaning more to solving systems using algebra because it is more accurate, don't have to worry about trying to make the whole function fit on the graph. @jim_thompson5910

Answer 19

2) Solve your system by graphing. Make sure that you detail the steps you took and include an image of the graph.

so they want you to find the solutions using graphing

Answer 20

each solution is a point

Answer 21

3) Solve your system algebraically (Elimination or Substitution). Make sure that you detail the steps and show your work.

that's when you use algebra to get the exact solutions

Answer 22

oh alright and #4 is what i think is easier @jim_thompson5910

Answer 23

or best

Answer 24

could you help with the algebra part?

Answer 25

by "best" I think it's a mix of what is convenient and what is accurate

Answer 26

we have x^2+8=y and 3x^2=y

Answer 27

since y = 3x^2, we can replace the y in the first equation with 3x^2

so...

x^2+8=y turns into x^2+8=3x^2

Answer 28

we could use the quadratic formula, but we can also just isolate x^2, and then isolate x

x^2+8=3x^2

x^2+8-x^2=3x^2-x^2

8 = 2x^2

2x^2 = 8

x = ???

Answer 29

so use the substitution method

Answer 30

yeah

Answer 31

x= 2,-2 @jim_thompson5910

Answer 32

if x = 2, then y = ???

Answer 33

which equation do i put 2 into? y=3x^2? @jim_thompson5910

Answer 34

either one works

Answer 35

y=3(2)^2
y=3*4 which is 12 so y=12 @jim_thompson5910

Answer 36

yeah so one ordered pair solution is (2,12)

Answer 37

you'll notice that the two graphs cross at (2,12)

what is the other ordered pair solution?

Answer 38

(-2,12) @jim_thompson5910

Answer 39

yes

Answer 40

so you can see that graphically works easiest if the two functions intersect at points that have whole numbered coordinates

Answer 41

ok! and algebra is easiest when fractions and decimals come into play... @jim_thompson5910

Answer 42

yeah or radicals (or anything like that)

Answer 43

wowww. never thought i would hear myself say algebra was easier at times lol @jim_thompson5910

Answer 44

lol I'm glad you think so

Answer 45

Thanks for your help! @jim_thompson5910

Answer 46

you're welcome