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/sci/ - Science & Math

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4609778 No.4609778 [Reply] [Original]

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Hey /sci/! Doing my math homework, 8th grade honors and am stuck, hopeing someone could help me out with this?
I need to solve the system of equations by the substitution method.

y=3x+1
3y-4x=13
How I solved it (not sure if this is correct)
3(3x+1)-4x=13
9x+3-4x=13
combined like terms..
5x+3=13
Subtract 3 from both sides
5x=10
divide 10 by 5
=2

I think I know what im doing, but just wanted to double check. Thanks everyone.

>> No.4609788

y=3x+1
3y-4x=13

3(3x + 1) - 4x = 13
9x-4x + 3 = 13
5x = 10
x = 2

You were right

>> No.4609790

Yeah, typically you can solve equations if you have the same number of equations as you do unknowns, in this case you had two starting equations, two unknowns, so classic substitution is the way to go.

>> No.4609794

>>4609788
Excellent! Thank you very much, one more question since I have someone with knowledge...

Same scenario, I need to solve the system of quations by the substitution method, any idea what to do if y or x is not already solved?

16x+4y=13
-4x=y+8

this is the last problem, and I am totally stumped. =[

>> No.4609797

>>4609790

Thank you for responding, greatly appreciated.

>> No.4609805

>>4609790
>>4609788
Any idea what to do if it's asking for an ordered pair? for that first problem? I went back and looked at the directions for it, but I don't see how it could become an ordered pair... Unless I substitute the 2 we got from X into the first equation...hmmm.

>> No.4609807

>>4609790
I disagree substitution problems get mess fast

-y + 3x = -1
3y -4x = 13

(-y + 3x = -1)*3 = -3y + 9x = -3

-3y + 9x = -3
+3y -4x = 13
-----------------
0y + 5x = 10

subtraction method or whatever its called could be quicker depending on the values

>> No.4609808

>>4609794
solve for it.


-4x=y+8

either

-8-4x = y

or

-y/4-2 = x

>> No.4609809

>>4609794

just use algebra to solve y or x
-4x=y+8
becomes
y = -8 - 4x

>> No.4609812

>any idea what to do if y or x is not already solved?
solve for it duh.

-4x=y+8(easier one)
0 = y + 8 + 4x
-y = 8 + 4x
y = -8 - 4x

>> No.4609819

>>4609807

That's a pretty relative term, solving for one variable and moving from there will always bring you to your solutions no matter what problems you have - ordered pairs are great when you can actually see that they cancel each other out so neatly, but when that's not the case, you must take straightforward methods in order to guarantee a solution.

>> No.4609823

>>4609778
Look man, to save you from any future embarrassment you should refrain from posting here with homework help threads, people aren't usually this friendly so instead use something like:

www.wolframalpha.com
or if you want the method explained to you, then use google/ your teacher/ www.khanacademy.org

>> No.4609838

>>4609819
>>4609807
Matrices always win

>> No.4609850
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4609850

>>4609838

Dispute settled

>> No.4609934
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4609934

>>4609778
8th grade huh? Do you guys know matrices yet? I don't think so. If not the best way is substitution or combinations.

However, once you learn matrices I highly suggest using them whenever applicable. If you go into any respectable field, matrices are your best friend.