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OpenStudy (song_of_the_sole):
solve the system by substitution
OpenStudy (song_of_the_sole):
-4.5x-2y=-12.5
3.25x-y=-0.75
jimthompson5910 (jim_thompson5910):
hint: solve for y in the second equation
OpenStudy (song_of_the_sole):
how do i do that
jimthompson5910 (jim_thompson5910):
how would you move the 3.25x over?
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OpenStudy (song_of_the_sole):
subtract it?
jimthompson5910 (jim_thompson5910):
subtract 3.25x from both sides, yes
jimthompson5910 (jim_thompson5910):
giving you what?
OpenStudy (song_of_the_sole):
-4
jimthompson5910 (jim_thompson5910):
-0.75 and -3.25x are NOT like terms
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OpenStudy (song_of_the_sole):
-4x?
jimthompson5910 (jim_thompson5910):
you can't combine them
jimthompson5910 (jim_thompson5910):
just leave it as -0.75-3.25x
OpenStudy (song_of_the_sole):
so -y=-0.75-3.25
jimthompson5910 (jim_thompson5910):
-y=-0.75-3.25x
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jimthompson5910 (jim_thompson5910):
then we multiply both sides by -1. Why? To turn that -y into +y which is just y
so we'd go from
-y=-0.75-3.25x
to
y=0.75+3.25x
every negative flips to a positive
OpenStudy (song_of_the_sole):
ok
OpenStudy (song_of_the_sole):
then what?
jimthompson5910 (jim_thompson5910):
now we plug that into the first equation
\[\Large -4.5x-2y=-12.5\]
\[\Large -4.5x-2*(y)=-12.5\]
\[\Large -4.5x-2*({\color{red}{y}})=-12.5\]
\[\Large -4.5x-2*({\color{red}{0.75+3.25x}})=-12.5\]
\[\Large -4.5x-2*(0.75+3.25x)=-12.5\]
\[\Large -4.5x-2*(0.75)-2(3.25x)=-12.5\]
\[\Large -4.5x-1.5-6.5x=-12.5\]
I'll let you solve for x
OpenStudy (song_of_the_sole):
-2x=-11
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jimthompson5910 (jim_thompson5910):
how did you get -2x?
OpenStudy (song_of_the_sole):
i added -4.5 to -6.5
OpenStudy (song_of_the_sole):
or would i just combine
jimthompson5910 (jim_thompson5910):
-4.5 plus -6.5 does not equal -2
OpenStudy (song_of_the_sole):
-11
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jimthompson5910 (jim_thompson5910):
so we have -11x = -11 which means x = ???
OpenStudy (song_of_the_sole):
1
jimthompson5910 (jim_thompson5910):
now plug that into y=0.75+3.25x
OpenStudy (song_of_the_sole):
ok....
OpenStudy (song_of_the_sole):
what would that look like??
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jimthompson5910 (jim_thompson5910):
replace x (in `y=0.75+3.25x`) with 1
OpenStudy (song_of_the_sole):
no which equation
jimthompson5910 (jim_thompson5910):
y=0.75+3.25x
OpenStudy (song_of_the_sole):
oh so y=0.75+3.25(1)
jimthompson5910 (jim_thompson5910):
yes
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OpenStudy (song_of_the_sole):
it will still be y=0.75+3.25
jimthompson5910 (jim_thompson5910):
0.75+3.25 = ???
OpenStudy (song_of_the_sole):
4
jimthompson5910 (jim_thompson5910):
so x = 1 and y = 4
OpenStudy (song_of_the_sole):
oh is that all?
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