Question

Would anyone be so gracious as to helping me get a better understanding of the dreadful algebra!??!?!!? :)

Explain, in complete sentences, how you would use the elimination method to solve the following system of equations. Provide the solution to the system.

2x + 9y = 4
3x + 7y = -7

Answer 1

1st you want to figure out which variable you want to solve

Answer 2

X

Answer 3

ok. oh n btw i replied. the answer is A!!! fromt he previous question

Answer 4

thank you love!!!! :)))))))))))) I got that answer after I "closed" the question box

Answer 5

i said it 2 times. lol anywayz let do this problem

Answer 6

thank you nonetheless! ok let's go!

Answer 7

Hey, an intermission, if you would oblige me...
if
x = y, then
ax = ay
right?

Answer 8

And if
a = b
and
c = d

then

a + c = b + d


Don't worry, these are relevant, we'll use them.

Answer 9

Thank you kind sir....! @terenzreignz

Answer 10

man i hate the ax=ay method

Answer 11

So you have
2x + 9y = 4

From our first rule, we can get
7(2x + 9y) = 7(4)
14x + 63y = 28, let's stop here, and call this "equation 1"

You also have
3x + 7y = -7

Again, from our first rule, we can get
-9(3x + 7y) = -9(-7)
-27x - 63y = 63, stop here again, call this "equation 2"

Are you getting it so far?

Answer 12

Yes, I've gone thru this a time before! But one question, how did you get the "7" in 7(2x+9y)

Answer 13

If you don't mind me asking.....! :))

Answer 14

Here's a joke: Subway called, they want their 6 inch back ;)

Answer 15

LOL

Answer 16

Another joke/flattery I made up: Verizon called, they want their "SMART" phone back

Answer 17

Ok... You said you wanted to solve for x first (personally, I'd have gone for y first)
So, we have to somehow get rid of the y.

To do that, you have to make it so that the coefficient (the number that goes beside the letter) of the y in the first equation is equal to the NEGATIVE of the coefficient of the y in the second equation.
In the first equation, the coeff of y was "9" and in the second, it was "7"
You need to get what's called their "least common multiple"
And that's 63.
63/9 is 7, so that's what I multiply to the first equation.
63/7 is 9, so that's what I multiply to the second equation, and then I NEGATED it (multiplied it by -1)

Answer 18

You'll see why this is done, when I proceed... shall I?

Answer 19

please do lol

Answer 20

oh my god....this is actually making sense!!!!! :')

Answer 21

Remember our second rule?
if
a=b
and
c=d
then
a+c = b+d
?

We'll just apply that, on a larger scale, sort of...

Answer 22

I remember! I will, I promise!

Answer 23

All right,
equation 1:
14x + 63y = 28

equation 2:
-27x - 63y = 63

Remember these?

Answer 24

I do, yes

Answer 25

Now we use the second rule, we add both expressions on the left, and equate them to the sum of the expressions on the right:
14x + 63y - 27x - 63y = 28 + 63

Answer 26

Notice something?

Answer 27

combine like term *cough**cough*

Answer 28

I'm writing down the steps to refer to, but yes, I notice that in order to prolong the steps, I'll have to combine

Answer 29

and...?

Answer 30

Get x by itself

Answer 31

And then you'll have reduced it to a linear equation in one variable. Solve for x, and you're almost done! Just substitute that x which you get for the x in either one of the equations you started with, and then solve for y, and then you'll be done!

Answer 32

oh my....I appreciate your efforts!!

Answer 33

I appreciate your appreciation; have fun! :)

Answer 34

I will never have fun with math, but thank you:)