Question

What is the solution(s) to the following system of equations?
y = x2 + 4x + 9
y = x2 + 3x + 8

(4, 3)

(–1, 6)

(–1, 2)

(4, 8)

Answer 1

Does x2 mean \[\large x^2\]?

Answer 2

Add both of the lines together, and solve for y. then plug in the x value from each of the answer until one gives the correct y value.

Answer 3

@GoldPhenoix yes

Answer 4

\[(x ^{2}+4x+9) + (x ^{2}+ 3x+8)\]

Answer 5

is that how i add them together?

Answer 6

yup and you have to add the y together too, so you'll get 2y = that. simplify and divide both sides by two.

Answer 7

do i add them together by foiling?

Answer 8

Foiling is only used for multiplying polynomials. You can just add the like terms.

Answer 9

okay, so how would i add x^2 + x^2?

Answer 10

x^2+x^2=(1+1)x^2 = 2x^2

Answer 11

\[2y=2x ^{2}+7+17\]

Answer 12

is that right so far?

Answer 13

7x but yes. Now divide by 2 and just plug in and you'll get the answer.

Answer 14

\[y=x ^{2}+3.5x+\]

Answer 15

whoops, plus 8.5 at the end

Answer 16

\[y=x ^{2}+\frac{ 7 }{ 2 }x+\frac{ 17 }{ 2 }\]

Answer 17

what you have done so far is wrong..

Answer 18

if you want to solve this by substitution,
you can choose to put the 1st eqn into the 2nd eqn.
so wherever you see "y" in the second eqn, place the 1st eqn there..

Answer 19

http://sketchtoy.com/37164441

Answer 20

do you understand what i have done?

Answer 21

ohh okay and then you would plug that -1 into the other equation for x?

Answer 22

or either of the equations?

Answer 23

yes...but you rather plug in -1 which is the value of x into either of the equations to find the value of y.

Answer 24

\[-1^{2}+49-1)+9= -1^{2}+3(-1)+8\]

Answer 25

oops i didnt mean 49

Answer 26

i meant to put + 4(-1)

Answer 27

\[-1+4(-1)+9=-1^{2}+3(-1)+8\]

Answer 28

i meant you could put the value of x in either of the eqns.
so
\[\Large y=(-1)^2+4(-1)+9\]
\[\Large y=??\]

Answer 29

you get the same value when you plug it into the other eqn.

Answer 30

y= 14?

Answer 31

no..

Answer 32

6?

Answer 33

yes!

Answer 34

so is it the second one?

Answer 35

yes..

Answer 36

thank you!

Answer 37

yw...(:

Answer 38

@kausarasalley, The method I told him to do works fine.

Answer 39

@JBrandonS
do you get the correct answer when you use your method?

Answer 40

yes.