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.

Question

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.

freckles · Answer

Like x+6=3
?

freckles · Answer

oh system?

freckles · Answer

2 variables?

nikkibxox · Answer

Like   

    2x – 3y = –2
    4x +   y = 24

freckles · Answer

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

freckles · Answer

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

freckles · Answer

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

nikkibxox · Answer

y=4x+24?

freckles · Answer

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 · Answer

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 · Answer

Makes sense.

freckles · Answer

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 · Answer

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

freckles · Answer

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 · Answer

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

nikkibxox · Answer

Wait. It would be +12

freckles · Answer

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

nikkibxox · Answer

Yes.

freckles · Answer

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

nikkibxox · Answer

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

freckles · Answer

groovy

freckles · Answer

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

freckles · Answer

y=-4x+24
this one!

nikkibxox · Answer

Yeah. Plug it in?

freckles · Answer

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 · Answer

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

nikkibxox · Answer

y=4

freckles · Answer

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

freckles · Answer

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This was the system .