How do you solve a system of equations? I don't have a specific equation that needs to be solved I just need help figuring it out. I cant seem to get it. Medal... Fan...Everything... Thanks.

- NikkiBxox

- jamiebookeater

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- freckles

Like x+6=3
?

- freckles

oh system?

- freckles

2 variables?

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## More answers

- NikkiBxox

Like
2x – 3y = –2
4x + y = 24

- freckles

well there are a couple of ways to go about it:
elimination, substitution, ..

- freckles

Like you can solve the second equation for y.
Use that y in the first equation then solve for x.

- freckles

So first can you isolate y in the following equation:
4x+y=24

- NikkiBxox

y=4x+24?

- freckles

Remember whatever you do to one side you must do to the other...
You subtracted 4x on the left hand side but added 4x on the right hand side..
It should have been you subtracted 4x on both sides.

- freckles

4x+y=24
subtract 4x on both sides
4x+y-4x=24-4x
the whole point of this is to get y on the left hand side by itself
4x-4x=0
so you have
y=24-4x
also can be written as
y=-4x+24

- NikkiBxox

Makes sense.

- freckles

2x – 3y = –2
now we are going to take that y we just found in terms of x
and insert in the first equation
2x-3(-4x+24)=-2
Solve this for x.

- NikkiBxox

One question would i distribute the -3 to the parenthesis? Or just to PEMDAS

- freckles

you have to distribute
the distributive property says a(b+c)=ab+ac
then you can apply order of operations with common terms on the left hand side

- NikkiBxox

Got it.
2x-12-72=-2
-10x-72=-2
-10=70
x=-7

- NikkiBxox

Wait. It would be +12

- freckles

so you mean to say
2x+12x-72=-2 ?

- NikkiBxox

Yes.

- freckles

ok and this equation 2x+12x-72=-2 is right so far

- NikkiBxox

If I refigure that it would be
2x+12x-72=-2
+72 +72
2x+12x=70
14x=70
x=5

- freckles

groovy

- freckles

now remember that one equation that we solved for y in terms of x...?

- freckles

y=-4x+24
this one!

- NikkiBxox

Yeah. Plug it in?

- freckles

you can finally find y now by inputting the x you just found into this equation
(you could also used the other equation; it just seems easier to plug into this one because we already have y isolated)

- freckles

and yes
so you have
y=-4(5)+24

- NikkiBxox

y=4

- freckles

This method we used was called substitution.
Let me show you elimination on this problem.

- freckles

|dw:1444618292337:dw|
This was the system .

- freckles

To do elimination, we need to choose something to multiply one of the equations (or even both) by so we can get either the x terms to be opposites or the y terms to be opposites
What opposite means is like, the opposite of 4x is -4x or the opposite of -3y is 3y. Notice the sign is the only thing that is different when we use the word opposite.

- freckles

now we could go about this in two very simple ways

- freckles

we could multiply the first equation by -2
or
we could multiply the second equation by 3
but do not do both

- freckles

|dw:1444618467505:dw|
notice if we choose to multiply both sides of the second equation by 3 we have the above

- NikkiBxox

That makes a lot of sense!!

- freckles

notice we have -3y is the opposite of 3y
when you add opposites you get 0
that is why we wanted opposites

- freckles

so we are going to add the equations together
2x-3y=-2
12x+3y=72
-----------
14x+0y=70
14x+0=70
14x=70
do you see we eliminated the y?

- freckles

you solved this exact same equation above and got x=5

- NikkiBxox

Yes. They are opisites.....OH okay!!

- freckles

now using either equation you can find y

- freckles

|dw:1444618634766:dw|
I like this equation because there is only 1 being multiplied to the y

- freckles

so input 5 for x:
4(5)+y=24
20+y=24
y=4

- freckles

you could have used the first equation though and got y is 4
2x-3y=-2
2(5)-3y=-2
10-3y=-2
-3y=-12
y=4

- freckles

see!?

- NikkiBxox

Yes!! Thank you so much!!

- freckles

np

- freckles

you can also graph the equations and find the intersection
i don't really like this method because the solutions aren't always integer pairs like this solution we got for this one

- NikkiBxox

Okay. I kinda get how to do that one. These seem easier by far.

- freckles

you can solve this one if you want to test yourself:
a+2b=5
5a-b=6

- NikkiBxox

I definintaly will in the morning. Its time for sleep. Thanks again!

- freckles

np
if you put your work here whenever you get a chance and tag me and also message me (just to make sure I see it do both), I will check your work

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