Question

HELP~ SYSTEM OF EQUATIONS Q?

Answer 1

Ralph wants to find the solution to a system of equations using y = x - 2 and y = x2 + 6x - 38. Joey says that Ralph can solve x2 + 5x - 36 = 0 to find the x coordinates of the solutions to his system. Explain and demonstrate why Joey is correct

Answer 2

Oh equality...
It has so many strange... qualities LOL

Answer 3

Okay... more to the point,
suppose we have
a = b
and
m = n

follow?

Answer 4

lol..yeah I'm following. :)

Answer 5

Well then, it shouldn't matter to the first equation if we subtract m from both sides, right?
a - m = b - m

Answer 6

You mean to set the y='s to equal each other?

Answer 7

You could do that too ^_^

Answer 8

So then you'll get...?
What equation?

Answer 9

y = x - 2 = x^2 + 6x - 38 ?

Answer 10

Okay, and do away with the y in the very left sideand stick to
\[\large x-2 = x^2 + 6x - 38\]
Now, subtract x-2 from both sides.

Answer 11

Ok, I don't know how to put x -2 into the right side. But the left then is 0

Answer 12

-(x - 2)

Answer 13

Or do it one at a time--
subtract x
and then subtract -2 (means add 2)

Answer 14

oh, ok..
X + 6 - 38 ?
I'm not sure how to add 2 to the x.

Answer 15

You can only add or subtract similar terms.

Answer 16

Sorry I'm not good at these.:(
So x + 12 - 76 ?

Answer 17

You can only add or subtract terms IF they have the EXACT same set of variables attached to them.

Answer 18

Actually, where did 12 and 76 come from?

Answer 19

Well, I first had x + 6 - 38, so I multiplied the 6 and -38 by 2. ?

Answer 20

You did NOT have x + 6 - 38
You had
\[\Large x^{\color{red}2}+ 6\color{red}x - 38\]

Answer 21

Yes, and then I subtracted x like you said. Do I just add 2?

Answer 22

You subtract x, and then you get...?

Answer 23

You can only subtract x from 6x.

Answer 24

Oh, 5x, right?

Answer 25

yup.
now add the 2 to the -38
Be careful with signs now.

Answer 26

cool, so x^2 + 5x - 36?

Answer 27

yes.. equals zero on the other side.
And that's it.

Answer 28

Oh, lol I just realized that equals the third equation! Thanks so much, I get it now:)