Question

Which pair of points represents the solution set of this system of equations?
y = x2 − 6x + 8
2y + x = 4

Answer 1

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Answer 2

yes maam a(2, 1) and (4, 0), b(1.5, 1.25) and (4, 0), c(0, 0) and (5, -5), d(-1.25, -2.75) and (1.25, 3), eThere is no real solution

Answer 3

So each option has 2 coordinates correct?

Answer 4

yes

Answer 5

Ok, I think the easiest way to go about this is substitution method. Are you familiar with this?

Answer 6

I have used it once or twice but i never really learned it

Answer 7

Ok, we have 2 equations, \(\bf y=x^2-6x+8\) and \(\bf 2y+x=4\) right?

Answer 8

yes

Answer 9

Ok, so now, since one of the equations is y=...., we can substitute that in for y on the second equation which gives us \(\bf 2(x^2-6x+8)+x=4\). Are you following so far?

Answer 10

Do you get that?

Answer 11

ya i get it

Answer 12

Ok, now, can you distribute the 2?

Answer 13

\[(2x ^{2}-12x+16)+x=4\]

Answer 14

Yep, but we don't need the parentheses anymore

Answer 15

okay

Answer 16

So now we have \(\bf 2x^2-12x+16+x=4\) which can be simplified to \(\bf 2x^2-11x+16=4\)

Answer 17

okay

Answer 18

Now, subtract 16 from each side.

Answer 19

\[2x ^{2}-11x=-12\]

Answer 20

Yep, what do you think you will do next? Remember, we are trying to get x by itself

Answer 21

zero product property??

Answer 22

We will need to divide by -11.

Answer 23

2x^2-x=1.09?

Answer 24

Since we divided by -11, it will be +x

Answer 25

oh okay

Answer 26

Let me try something different really quick

Answer 27

alrighty

Answer 28

Hmmmm, maybe @SolomonZelman can help out?

Answer 29

You could also substitute the options in if you wanted.

Answer 30

\(\large\color{black}{ y = x^2 - 6x + 8 }\)
\(\large\color{black}{ 2y + x = 4 }\)

\(\large\color{black}{ y = x^2 - 6x + 8 }\)
\(\large\color{black}{ x = 4- 2y }\)

\(\large\color{black}{ y = (4- 2y)^2 - 6x + 8 }\)

Answer 31

Use: \(\large\color{red}{ (a-b)^2=a^2-2ab+b^2 }\) to expand the \(\large\color{black}{ (4- 2y)^2 }\)

Answer 32

@sleepyjess
you were close back there with this equation:

So now we have 2x 2 −12x+16+x=4 which can be simplified to 2x 2 −11x+16=4

However - you then went to assume that you can get x on its own, but this is a quadratic so you cannot directly simplify it.

Rearrange to
2x 2 −11x+12=0

then use the quadratic formula to solve

Answer 33

OH

Answer 34

Or since it can be factored, that method is also an option.

Answer 35

(2x - 3) (x - 4) = 0 is the factors of 2x^2 - 11x + 12 = 0