it would be a lot easier if you posted one question at a time, but I'll try
OpenStudy (anonymous):
okay hold on please
OpenStudy (bloomlocke367):
okay
OpenStudy (anonymous):
question 1
Two lines, A and B, are represented by the equations given below:
Line A: 2x + 2y = 8
Line B: x + y = 4
Which statement is true about the solution to the set of equations?
It is (8, 4).
It is (4, 8).
There is no solution.
There are infinitely many solutions.
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OpenStudy (anonymous):
is that better?
OpenStudy (anonymous):
☺
OpenStudy (bloomlocke367):
yes :)
OpenStudy (bloomlocke367):
okay, I know there's an easier way to solve it, but I've always been better with substitution. Do you know what that is?
OpenStudy (anonymous):
it doesn't say
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OpenStudy (bloomlocke367):
okay, well we can solve the second equation for y, so it would be y=4-x. you then would plug that in for y in the first equation and you'd have \(2x+2(4-x)=8\). do you see what I did?
OpenStudy (anonymous):
sort of
OpenStudy (bloomlocke367):
what don't you get?
OpenStudy (anonymous):
I don't know how to to do this very well so it is confusing to me how you get from y=4-x
too 2x+2(4−x)=8
OpenStudy (anonymous):
are you still there
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OpenStudy (bloomlocke367):
okay, you know how it was \(2x+2\color{red}y=8\). well, the other equations was \(\color{red}{y=4-x}\). so you plug it in for y.. and you get \(2x+2\color{red}{(4-x)}=8\)
OpenStudy (bloomlocke367):
does that make more sense?
OpenStudy (anonymous):
yes!
OpenStudy (bloomlocke367):
okay. now just solve for x, do you know how?
OpenStudy (anonymous):
not really
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OpenStudy (bloomlocke367):
okay, you're going to want to first use the distributive property.. do you know how to do that? when you have \(2(4-x)\) you distribute the 2 to each of the terms. so you need to do \(2\times4\) and \(2\times-x\)
OpenStudy (anonymous):
2x4=8 2x2=4
OpenStudy (bloomlocke367):
why'd you do \(2\times2\)?
OpenStudy (anonymous):
oh sorry they cancel
OpenStudy (anonymous):
is that right
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OpenStudy (anonymous):
hello
OpenStudy (bloomlocke367):
I'm here.
OpenStudy (bloomlocke367):
I'm still confused as to why you did 2*2..
OpenStudy (anonymous):
k
OpenStudy (anonymous):
i thought it was just multiplying but then i remembered that you have to cancel
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OpenStudy (anonymous):
one of them
OpenStudy (bloomlocke367):
after you distribute you should have \(2x+8-2x=8\)
OpenStudy (anonymous):
oaky
OpenStudy (anonymous):
okay
OpenStudy (bloomlocke367):
now can you solve that?
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OpenStudy (anonymous):
how
OpenStudy (anonymous):
im really sorry i really have no idea how to do this
OpenStudy (bloomlocke367):
okay, well the first thing to do is combine like terms. what's \(2x-2x\)?
OpenStudy (anonymous):
0 ?
OpenStudy (bloomlocke367):
yes, but for now, we're going to say \(0x\) so we don't get confused. and what's \(8-8\)?
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OpenStudy (anonymous):
0
OpenStudy (bloomlocke367):
yes, so you have \(0=0\) correct?
OpenStudy (anonymous):
yup
OpenStudy (anonymous):
so no solution
OpenStudy (bloomlocke367):
no, no solution would be if you had an answer that's undefined or something that was untrue, like 2=6
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OpenStudy (anonymous):
oh okay
OpenStudy (bloomlocke367):
so do you know what it is now?
OpenStudy (anonymous):
infinite
OpenStudy (bloomlocke367):
Yep!
OpenStudy (anonymous):
yeah!!! woooooh!!
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