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Like x+6=3 ?
Like 2x – 3y = –2 4x + y = 24
well there are a couple of ways to go about it: elimination, substitution, ..
Like you can solve the second equation for y. Use that y in the first equation then solve for x.
So first can you isolate y in the following equation: 4x+y=24
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.
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
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.
One question would i distribute the -3 to the parenthesis? Or just to PEMDAS
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
Got it. 2x-12-72=-2 -10x-72=-2 -10=70 x=-7
Wait. It would be +12
so you mean to say 2x+12x-72=-2 ?
ok and this equation 2x+12x-72=-2 is right so far
If I refigure that it would be 2x+12x-72=-2 +72 +72 2x+12x=70 14x=70 x=5
now remember that one equation that we solved for y in terms of x...?
y=-4x+24 this one!
Yeah. Plug it in?
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)
and yes so you have y=-4(5)+24
This method we used was called substitution. Let me show you elimination on this problem.
|dw:1444618292337:dw| This was the system .
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.
now we could go about this in two very simple ways
we could multiply the first equation by -2 or we could multiply the second equation by 3 but do not do both
|dw:1444618467505:dw| notice if we choose to multiply both sides of the second equation by 3 we have the above
That makes a lot of sense!!
notice we have -3y is the opposite of 3y when you add opposites you get 0 that is why we wanted opposites
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?
you solved this exact same equation above and got x=5
Yes. They are opisites.....OH okay!!
now using either equation you can find y
|dw:1444618634766:dw| I like this equation because there is only 1 being multiplied to the y
so input 5 for x: 4(5)+y=24 20+y=24 y=4
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
Yes!! Thank you so much!!
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
Okay. I kinda get how to do that one. These seem easier by far.
you can solve this one if you want to test yourself: a+2b=5 5a-b=6
I definintaly will in the morning. Its time for sleep. Thanks again!
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