Question

This is the only question on the entire quiz I don't get. Will fan + medal, please help!!!

A student is trying to solve the system of two equations given below:

Equation P: x + y = 8
Equation Q: 2x + 5y = 24

Which of the following steps can be used to eliminate the x term?

2(x + y = 8)
−2(x + y = 8)
−1(2x + 5y = 24)
−2(2x + 5y = 24)

Answer 1

what does it mean to eliminate something?

Answer 2

@amistre64 To get rid of?

Answer 3

yeah, or in math terms .. make it go to zero

Answer 4

so, what are our x terms in this case?

Answer 5

@amistre64 2x and x?

Answer 6

youre doing fine, yes

now, what would you propose we do to eliminate them?

what would we multiply one by such that when we add them together we get zero?

Answer 7

I wanna say 8 because if we're multiplying 1, 1 x 8 is 8. But at the same time I feel like that's wrong?

Answer 8

hmm, 8 isnt in our options so your feeling is spot on ...

let "n" be some number such that:

2x + nx = 0, fpr all values of x

(2+n)x = 0

any more ideas?

Answer 9

Oh! I was looking at the first equation. Would it be 5 then?

Answer 10

Or 2? Since we're trying to get rid of the x...(I'm sorry I know I'm really slow in math)

Answer 11

2 is closer :) lets try it out

(2+2)x = 0

4x = 0, this is not true for all x

when is 2+n = 0 ?

Answer 12

2+n = 0 when n = -2, right?

Answer 13

that better, yes

so what this tells us is that we want to multiply by a -2

the last thing to determine is which equation should we multiply by -2?

Answer 14

Equation Q because if we solve that one first we can just replace the x and y variables in question P?

Answer 15

well, equation Q already has 2x in it ... so we really want to leave it as is. this leaves us with equation P.

-2(x+...) = -2x + ...

now when we combine (add) -2P and Q we get

-2x + ...
2x + ...
---------
0x + ...

and our x term has been eliminated.

Answer 16

so, which option should we pick now?

Answer 17

B?

Answer 18

hmm, your post does not letter them, but i would agree with the second option yes

Answer 19

Oh, sorry! Also do you mind if I save this? Like your responses? You helped me a lot

Answer 20

save what you want :)

Answer 21

Thank you for helping me!!!

Answer 22

youre welcome, and good luck :)