i need math homework help?

Question

i have a huge math test tomorrow and i dont really understand it. the test is over solving systems with graphing, substitution, and elimination. i understand how to do the graphing and substitution, but not the elimination. so if someone could explain how to do this problem i would really appreciate it.

2x + 5y = 21
4x -y = 9

use the elimination method.

Answer 1

Alright for the elimination method you have to eliminate one of the variables. It does not matter if you choose x or y but just take whichever is easier.

2x + 5y = 21
4x -y = 9

In this case you can take x.

Multiply the first line by 2.

Now you have:

4x+10y=42
4x-y=9

Don't forget to multiply all the numbers in the equation. Now you can subtract the second line from the first one.

and you get 11y=33
Solve for y.
y=3 (divided by 11)

Now you replace y=3 into either of the equations.

4x-3=9
4x=12
x=3

Hope this helps. :) good luck on your test.

Answer 2

I'm hoping that by elimination, you mean linear combinations because that is the only other way i have learned to solve systems.
So heres how i would do it:
2x + 5y = 21 and
4x - y = 9
Alright, in order to solve this, its easier to get rid of the 'y' because there is already a 'y' variable by its self.(no coefficeint or number in front of it)
So in order to eliminate the 'y' variable, you have to make both 'y' variables in each equation opposite. (one has to negative and one has to be positive)
SO:
Leave the 2x + 5y = 21 alone
Then, multiply the ENTIRE EQUATION of 4x - y = 9 by 5 so that the 'y' will become -5y which will be the opposite of the other equation.
so then you are left with:
2x + 5y = 21 and
20x - 5y = 45
now add those two equations together....
22x +0y = 66 which simplifies into:
22x = 66
and you get that x=3
Now, substitute x=3 for one or both of the equations:
2(3) + 5y = 21
6 + 5y = 21
5y = 15
y = 3
To check, you may want to plug 'y' into the other equation so that it eqauls the same thing, so:
4(3) - y = 9
12 - y = 9
-y = -3 OR
y=3
So it works!
Hope this helps!!

Answer 3

Ironically, elimination method is the process that most students choose first in these situations. the main goal is to get either both the x or y coefficients to equal value but opposite sign so that when you add the 2 equations together, one variable is "eliminated". In your case you could either....

1) match the x values by multiplying the top equation by -2
-2(2x + 5y = 21) --> -4x - 10y = -42

now add that to the second equation and the x's will eliminate....

-4x - 10y = -42
4x - y = 9 +
---------------------------
0 - 11y = -33 ---->y=3, sub 3 back in for y in either of the original equations to find x.

2) or....you can eliminate the y's by multiplying 5 to the second equation. it would match up the coefficients while keeping the signs opposite.

5(4x - y) = 9 ----> 20x - 5y = 45

and add to top equation....

20x - 5y = 45
2x + 5y = 21 +
----------------------------
22x = 66 -------> x = 3, sub 3 back into x in either of the original equations to find y (it's merely coincidence that both x and y are 3 in this system).

Sometimes you have to multiply to both equations to reach a least common multiple....

2x + 3y = 6
3x + 4y = 4

the x's can "meet" at 6x or the y's at 12y (of course a negative must be multiplied to one of the equations as well to offset the signs.

Answer 4

Okaaayy. Let me attempt to explain. :D Math sucks doesnt it.
ok.
So you have
2x+5y=21
4x-y=9

What you first have to do is get rid of the 5y.
So you multiply EVERYTHING in the bottom problem by a number that will get the y to equal 5y. And since there is just a y...that means there is a 1 in front of it so you multiply everything by 5.

so THEN your problem looks like

2x+5y=21
20x-5y=45

then you can just cancel the 5y's because there is a positive and a negative and positives and negatives cancel each other.

ok...so after that you simply add down the columns.

2x = 21
20x = 45

so you add 2x and 20x to get 22x.
and you add 21 and 45 to get 66.

THEN. your problem looks like

22x=66
so you divide both sides by 22 and you are left with
x=3

Now i realize explaination over the computer is not the easiest thing but hey...i tried. :D.

I hope you get it.
good luck on the test! (i feel your pain)

Answer 5

Ok the one you gave me 2x+5y=21 and 4x-y=9
Elimination is wen you Eliminate one of the variables(x or y)
So its like adding...
2x+5y=21
+ 4x-y=9
___________

Right well then you have to eliminate and to cross out you need to make them the same number but different signs so you can do this...
2x+5y=21
(4x-y=9)5

Time all that in the parenthesis by 5

making it

2x+5y=21
20x-5y=45

YOu can now cross out the 5y and -5y cuz wen yu add them you get 0
so your left with

2x=21
20x=45
Now add down

22x=66
Then divide by 22
66/22 =3
x=3
then Plugg that into the equation and you will get y.
I KNOW ITS KINDA ALOT.

Answer 6

2x + 5y = 21
4x -y = 9


Take the first equation and find out what x equals:
1. 2x = 21 - 5y
2. x = (21 - 5y)/2

Take what you have for x (above) and subsitute it into the second equation (and find out what y equals):
1. 4 (21-5y)/2 - y = 9
2. 2 (21 - 5y) - y = 9
3. 42 - 10y - y = 9
4. 42 - 11y = 9
5. -11y = -33
6. y = 3

Now take your answer for y (above) and subtitute it into any of your original equations:
1. 2x + 5 (3) = 21
2. 2x + 15 = 21
3. 2x = 6
4. x = 3

So, answer:
x= 3, y =3