Question

find the solutions of the system y=x^2+3x-4 y=2x+2 I would prefer if you could walk me through the question rather than just give me the answer, but whatever you can do for me is appreciated

Answer 1

well do you know where to begin or have no idea

Answer 2

I was absent a couple of days this is a review I honestly have no clue what to do, I hate getting sick

Answer 3

lol no problem. well with any system the main objective is to find an x,y, etc. value that satisfies both equations

Answer 4

It's multiple choice if that helps at all, it seems I need two pairs of (x,y)

Answer 5

you can probably start by letting 2x+2=x^2+3x-4

Answer 6

So, I combine the two problems?

Answer 7

Then I need to find an (x,y) that will work for both?

Answer 8

Well, by setting the two functions equal to each other you can solve for the two values of x and plug each back into the equation to find the two corresponding y values

Answer 9

So I need to start by finding the two x's?
alright that should be pretty easy

Answer 10

yep, just factor and find the x values, then plug back in to find the y values.

Answer 11

I feel like there's no solution, but I don't want to say that, because the only reason I came to that conclusion is because I looked at the possible answers and none of them fit

Answer 12

what are the possible answers

Answer 13

A. (-3,6) and (2,-4)
B.(-3,-4) and (2,6)
C.(-3,-4) and (-2,-2)
D. No solution

Answer 14

because, either way -3 is in there, but neither -2 or 2 make them equal

Answer 15

the answer is b

Answer 16

But, the x's don't equal out..

Answer 17

oh, they don't have to equal. the sole purpose of setting the two equal to each other was to solve for the x values. once you have them, you plug back into either equation to solve for the y values

Answer 18

wait, so how would I know which x values go in there? Really sorry about this but I would greatly appreciate it, if you could walk me through all the steps, I'm definetly going to give you a medal

Answer 19

the x values you obtained satisfy both equations, so you can plug them into either one of the original functions to obtain the corresponding y values

Answer 20

Wait, how does it satisfy the equation, I'm so confused right now ;_;

Answer 21

So what I mean by satisfy the equation is this: a value for x that will make the equation true. so for example: after setting the two functions equal to each other and some algebra we get this: x^+x-6=0

so looking at this equation we see that it is equal to 0, so the question is: what values for x will make this equation true or what values will make the expression sum to 0

Answer 22

okay, if we have x^2+x-6=0 we need to make 0 with the 2 x factors? how does B make that 0 it would be -3^ = -9+2-6 that doesn't equal 0 and 2^2 = 4-3-6 also doesn't equal 0

Answer 23

unless we sub in y for the 0

Answer 24

so we factor and get x=2,-3

next we want to find our y values. well plugging these x values into to either of the original function will give us the two y values.

y=2x+2 ==> plug in x=2

y=2(2)+2=6

set 1= (2,6)

y=2x+2 ==> plug in x=-3

y=2(-3)+2=-4

set 2= (-3,-4)

Answer 25

The x values you found makes x^2+x-6=0

B is the set of x and y values that satisfy your original system of equation.

Here's how you check: lets take set 1=(2,6)

we can plug it in to either equation. Ill choose the easier one.

y=2x+2 ===> plug in set 1
6=2(2)+2

this set of numbers satisfies the equation
does that make sense?

Answer 26

I understand that it works in the main problem, but what I don't understand is how you said that the x values work for the other problem

Answer 27

what other problem? you mean x^2+x-6=0 ?

Answer 28

So what I mean by satisfy the equation is this: a value for x that will make the equation true. so for example: after setting the two functions equal to each other and some algebra we get this: x^+x-6=0

so looking at this equation we see that it is equal to 0, so the question is: what values for x will make this equation true or what values will make the expression sum to 0

Answer 29

You said that earlier how do the values for x make it = 0?
unless you're not supposed to sub them in in that problem

Answer 30

well, x^2-3x-1=8x-1

Answer 31

that turns into x^2-11x=0

Answer 32

Now that, that equals 0, we need to factor
and we get (0,11). Right?

Answer 33

So, now we put that into the main problems to find the y
y=0^2-0-1 y=-1
y=8(11)-1 88-1 y=87, so it's be answer b again (0,-1) and (11,87) right?

Answer 34

If so, then I understand it, and thank you

Answer 35

why do you think we set the two equations equal to each other?

Answer 36

To solve for the x values?

Answer 37

Well, either way number 11 was in the back of the book and it was answer b, so hank you I got it now I gave you a metal

Answer 38

yes, to solve for the x values that make x^2+x-6=0

now, x^2+x-6=(x+3)(x-2)=0

from here we can see that x=-3,2 satisfies the equation

but it is not so obvious for X^2+x-6=0 which is why you always have to factor polynomial equations

Answer 39

Omg, open study updates so slowly, I'm sorry but I closed the question

Answer 40

okay well goodluck

Answer 41

thank you, for the luck and the help.