sawq
  • 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...??
Mathematics
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SOLVED
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chestercat
  • chestercat
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pooja195
  • pooja195
What would you like to use?
pooja195
  • pooja195
I suggest elmination
sawq
  • sawq
Ok elimination then

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pooja195
  • pooja195
Keep this in mind: OPPOSITES CANCEL whats the opposite of 4 ?
sawq
  • sawq
-4
UsukiDoll
  • UsukiDoll
I second elimination method.. works best.
pooja195
  • pooja195
\[-4(-x + y = 27)\] distribute
sawq
  • sawq
4x + -4y = 27 ?
UsukiDoll
  • UsukiDoll
close but you forgot to distribute the -4 to the 27 what's -4 x 27?
pooja195
  • pooja195
i accidently slipped in the -
pooja195
  • pooja195
-4(x + y = 27) -4 * x = ? -4 * y = ? -4 * 27= ?
sawq
  • sawq
-108
UsukiDoll
  • UsukiDoll
we are distributing the -4 all over the first equation.
UsukiDoll
  • UsukiDoll
and yes -4 x 27 is -108 :)
sawq
  • sawq
-4x -4y -108
UsukiDoll
  • UsukiDoll
correct so your new first equation is -4x-4y=-108
pooja195
  • pooja195
ill let doll finish :)
UsukiDoll
  • UsukiDoll
so now we have -4x-4y=-108 4x + 1y = 45
UsukiDoll
  • UsukiDoll
what do we need to do to get rid of the x?
sawq
  • sawq
lol @pooja195 thanks for ur help
sawq
  • sawq
inverse? @UsukiDoll
UsukiDoll
  • UsukiDoll
umm .. not quite.. our goal is to eliminate a variable.
UsukiDoll
  • 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
  • sawq
ooh right so it would be: x - 5y = -63?
UsukiDoll
  • UsukiDoll
hmm .... only the right hand side of the equation is correct
UsukiDoll
  • UsukiDoll
ok... let's think finance for a bit you bought pens for $4, you paid $4 -4x+4x = ?
sawq
  • sawq
0x or just x
UsukiDoll
  • UsukiDoll
0x is fine... but 0 times x => 0
sawq
  • sawq
ohhhh
UsukiDoll
  • 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
  • UsukiDoll
oops I meant -4y+1y
sawq
  • sawq
3 dollars
sawq
  • sawq
so -3y
UsukiDoll
  • UsukiDoll
yes! so -4y+y = -3y
UsukiDoll
  • UsukiDoll
so now we have -3y=-63
UsukiDoll
  • UsukiDoll
all we need to do is isolate y ... how do we do that?
UsukiDoll
  • UsukiDoll
in other words... we need y by itself.. no numbers no variables..
sawq
  • sawq
divide -63/-3=21
UsukiDoll
  • UsukiDoll
mhm so y = 21
UsukiDoll
  • 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
  • UsukiDoll
x + y = 27
sawq
  • sawq
ok: x + 21 = 27 x= 6
UsukiDoll
  • UsukiDoll
yes
UsukiDoll
  • 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
  • UsukiDoll
4x + 1y = 45 so plug in x = 6 and y =21
sawq
  • sawq
4*6=24 1*21=21 21+24=45!!!
UsukiDoll
  • UsukiDoll
yes 21+24=45 45=45 so we have found our x and y values.
UsukiDoll
  • UsukiDoll
alternatively you can choose to eliminate the y first and solve for x
UsukiDoll
  • 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
  • UsukiDoll
^_^ I got the same values by eliminating the y first and my steps were shorter too.
sawq
  • sawq
Thanks a million @UsukiDoll you are the best!!!!! you really helped me
UsukiDoll
  • 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
  • UsukiDoll
:D you're welcome
sawq
  • sawq
gnite tysm

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