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What would you like to use?
I suggest elmination
Ok elimination then
Keep this in mind: OPPOSITES CANCEL whats the opposite of 4 ?
I second elimination method.. works best.
\[-4(-x + y = 27)\] distribute
4x + -4y = 27 ?
close but you forgot to distribute the -4 to the 27 what's -4 x 27?
i accidently slipped in the -
-4(x + y = 27) -4 * x = ? -4 * y = ? -4 * 27= ?
we are distributing the -4 all over the first equation.
and yes -4 x 27 is -108 :)
-4x -4y -108
correct so your new first equation is -4x-4y=-108
ill let doll finish :)
so now we have -4x-4y=-108 4x + 1y = 45
what do we need to do to get rid of the x?
umm .. not quite.. our goal is to eliminate a variable.
-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
ooh right so it would be: x - 5y = -63?
hmm .... only the right hand side of the equation is correct
ok... let's think finance for a bit you bought pens for $4, you paid $4 -4x+4x = ?
0x or just x
0x is fine... but 0 times x => 0
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?
oops I meant -4y+1y
yes! so -4y+y = -3y
so now we have -3y=-63
all we need to do is isolate y ... how do we do that?
in other words... we need y by itself.. no numbers no variables..
mhm so y = 21
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
x + y = 27
ok: x + 21 = 27 x= 6
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
4x + 1y = 45 so plug in x = 6 and y =21
4*6=24 1*21=21 21+24=45!!!
yes 21+24=45 45=45 so we have found our x and y values.
alternatively you can choose to eliminate the y first and solve for x
x + y = 27 4x + 1y = 45 -x-y=-27 4x+y=45 3x = 18 x=6 6 + y = 27 -6 -6 y=21
^_^ I got the same values by eliminating the y first and my steps were shorter too.
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.
:D you're welcome