- sawq

Urgent! Will fan and medal!!
x + y = 27
4x + 1y = 45
Whats the solution to the equations and how did u get it?
I know about substitution and elimination but its not working out... Help...??

- schrodinger

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- pooja195

What would you like to use?

- pooja195

I suggest elmination

- sawq

Ok elimination then

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## More answers

- pooja195

Keep this in mind: OPPOSITES CANCEL
whats the opposite of 4 ?

- sawq

-4

- UsukiDoll

I second elimination method.. works best.

- pooja195

\[-4(-x + y = 27)\]
distribute

- sawq

4x + -4y = 27 ?

- UsukiDoll

close but you forgot to distribute the -4 to the 27
what's -4 x 27?

- pooja195

i accidently slipped in the -

- pooja195

-4(x + y = 27)
-4 * x = ?
-4 * y = ?
-4 * 27= ?

- sawq

-108

- UsukiDoll

we are distributing the -4 all over the first equation.

- UsukiDoll

and yes -4 x 27 is -108 :)

- sawq

-4x
-4y
-108

- UsukiDoll

correct so your new first equation is
-4x-4y=-108

- pooja195

ill let doll finish :)

- UsukiDoll

so now we have
-4x-4y=-108
4x + 1y = 45

- UsukiDoll

what do we need to do to get rid of the x?

- sawq

lol @pooja195 thanks for ur help

- sawq

inverse? @UsukiDoll

- UsukiDoll

umm .. not quite.. our goal is to eliminate a variable.

- UsukiDoll

-4x-4y=-108
4x + 1y = 45
so what do we need to do to get rid of this x??
we have -4x and 4x... maybe adding these equations together might work

- sawq

ooh right so it would be: x - 5y = -63?

- UsukiDoll

hmm .... only the right hand side of the equation is correct

- UsukiDoll

ok... let's think finance for a bit
you bought pens for $4, you paid $4
-4x+4x = ?

- sawq

0x or just x

- UsukiDoll

0x is fine... but 0 times x => 0

- sawq

ohhhh

- UsukiDoll

ok so we got rid of the x... now for the y we have -4y+1
it's like you are trying to buy pens for $4, but all you have is a dollar. How much more money do you need?

- UsukiDoll

oops I meant -4y+1y

- sawq

3 dollars

- sawq

so -3y

- UsukiDoll

yes! so -4y+y = -3y

- UsukiDoll

so now we have -3y=-63

- UsukiDoll

all we need to do is isolate y ... how do we do that?

- UsukiDoll

in other words... we need y by itself.. no numbers no variables..

- sawq

divide -63/-3=21

- UsukiDoll

mhm so y = 21

- UsukiDoll

the second part is finding x.. luckily it's easier.. we just need to subsitute y = 21 in one of the original equations. I highly suggest the easier ones

- UsukiDoll

x + y = 27

- sawq

ok: x + 21 = 27
x= 6

- UsukiDoll

yes

- UsukiDoll

so x =6 and y =21, but do these values work for the other equation. I know it does for the first equation because
x+y=27
6+21=27
27=27

- UsukiDoll

4x + 1y = 45
so plug in x = 6 and y =21

- sawq

4*6=24 1*21=21
21+24=45!!!

- UsukiDoll

yes
21+24=45
45=45
so we have found our x and y values.

- UsukiDoll

alternatively you can choose to eliminate the y first and solve for x

- UsukiDoll

x + y = 27
4x + 1y = 45
-x-y=-27
4x+y=45
3x = 18
x=6
6 + y = 27
-6 -6
y=21

- UsukiDoll

^_^ I got the same values by eliminating the y first
and my steps were shorter too.

- sawq

Thanks a million @UsukiDoll you are the best!!!!! you really helped me

- UsukiDoll

I've noticed that through inspection I had two one y's so I figured if I make one of the y's negative I can solve this quickly.

- UsukiDoll

:D you're welcome

- sawq

gnite tysm

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