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OpenStudy (anonymous):
Solve each system by substitution
11. { 14x – 35 = 7y
-25 – 6x = 5y
14x – 35 = 7y
7(2x – 5) = 7y
y= 2x – 5
-25 – 6x = 5y
-6x – 5y – 25 = 0
y=(-6x – 25)
(-4,-7.5)
Solve each system by elimination.
13. { 2x + 3y = 4
4x + 6y = 9
2x = -3y + 4
x = (-3y+4)/2
4[(-3y+4)/2] - 9y = 9
2(-3y+4) - 9y = 9
-6y + 10 - 9y = 9
-15y = -1
y = 1/15
x = (-3y+4)/2
x = (-3(1/15)+4)/2
x = [(-1/5)+4/2
= (24/4)/2 = 12/5
Final Answer: y = -1/3 when x = 12/5
OpenStudy (anonymous):
oops can you see the whole equation for #11?
jimthompson5910 (jim_thompson5910):
I'm getting different answers for #11 and #13
jimthompson5910 (jim_thompson5910):
when you get to -6x – 5y – 25 = 0, plug in y = 2x – 5 and solve for x
-6x – 5y – 25 = 0
-6x – 5(2x-5) – 25 = 0
x = ???
OpenStudy (anonymous):
oh dang :/ I thought I finally knew how to solve these problems.. do you mind helping me? showing how you got your answers im so tired ive been working on these problems since 2 pm ugh
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jimthompson5910 (jim_thompson5910):
for #11, you got -6x – 5y – 25 = 0 correct
jimthompson5910 (jim_thompson5910):
now you plug in y = 2x - 5 and solve for x
jimthompson5910 (jim_thompson5910):
so you have to solve -6x – 5(2x-5) – 25 = 0
OpenStudy (anonymous):
for #11 I got
{ 14x–35=7y
-25–6x=5y
14x–35=7y
7(2x–5)=7y
y=2x–5
-25–6x=5y
-6x–5y–25=0
y=(-6x–25)
(-4,-7.5)
OpenStudy (anonymous):
all I am seeing are boxes?
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jimthompson5910 (jim_thompson5910):
refresh the page
jimthompson5910 (jim_thompson5910):
the boxes will go away
OpenStudy (anonymous):
okay got it :)
OpenStudy (anonymous):
they went away s:
jimthompson5910 (jim_thompson5910):
are you able to solve -6x - 5(2x-5) - 25 = 0
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OpenStudy (anonymous):
x=0?
jimthompson5910 (jim_thompson5910):
then you will use that value of x to find y
jimthompson5910 (jim_thompson5910):
x = 0
y = 2x - 5
y = ???
OpenStudy (anonymous):
y=2x-5=0
jimthompson5910 (jim_thompson5910):
if x = 0, then y is ...
y = 2x - 5
y = 2(0) - 5 ... replace every x with 0
y = ???
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OpenStudy (anonymous):
y=-5?
jimthompson5910 (jim_thompson5910):
yes
jimthompson5910 (jim_thompson5910):
so the answer to #11 is (0, -5)
jimthompson5910 (jim_thompson5910):
since you found that x = 0 and y = -5
OpenStudy (anonymous):
thank you soooo much!! :) do you mind helping me with #13 also?
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jimthompson5910 (jim_thompson5910):
notice your second equation in #13 is 4x + 6y = 9
jimthompson5910 (jim_thompson5910):
yet you somehow have
4[(-3y+4)/2] - 9y = 9
after you plugged in that x value. Where did the -9y come from?
jimthompson5910 (jim_thompson5910):
it should be
4[(-3y+4)/2] + 6y = 9
OpenStudy (anonymous):
I honestly don't know my friend was trying to help me :c
jimthompson5910 (jim_thompson5910):
I see
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OpenStudy (anonymous):
sorry I suck at math /: any other subject im good at lol
jimthompson5910 (jim_thompson5910):
thats ok
jimthompson5910 (jim_thompson5910):
are you able to compute 4[(-3y+4)/2]
jimthompson5910 (jim_thompson5910):
or simplify that
OpenStudy (anonymous):
yes hold on 2(4-3y)?
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jimthompson5910 (jim_thompson5910):
keep going
OpenStudy (anonymous):
simplify that answer also?
jimthompson5910 (jim_thompson5910):
distribute
OpenStudy (anonymous):
8-6y?
jimthompson5910 (jim_thompson5910):
4[(-3y+4)/2] + 6y = 9
turns into
8-6y + 6y = 9
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OpenStudy (anonymous):
thank you c: do I keep going? or is that the answer?
jimthompson5910 (jim_thompson5910):
keep going and try to solve for y
OpenStudy (anonymous):
y= 0?
jimthompson5910 (jim_thompson5910):
what is -6y + 6y
OpenStudy (anonymous):
I keep getting 0 on my calculator... 36y?
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jimthompson5910 (jim_thompson5910):
maybe think of it as 6y - 6y
jimthompson5910 (jim_thompson5910):
but yeah you get 0y or just 0
jimthompson5910 (jim_thompson5910):
8-6y + 6y = 9
turns into
8+0 = 9
and that becomes
8 = 9
jimthompson5910 (jim_thompson5910):
but I'm sure you see the problem
OpenStudy (anonymous):
thank you again I really appreciate you helping me! c:
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jimthompson5910 (jim_thompson5910):
so what's the answer to #13?
OpenStudy (anonymous):
(9,0)?
jimthompson5910 (jim_thompson5910):
is 8 = 9 true?
OpenStudy (anonymous):
no
jimthompson5910 (jim_thompson5910):
since it's always false, regardless of what x and y are, this means that the overall system has no solutions at all. There's no way to make that equation true.
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jimthompson5910 (jim_thompson5910):
visually, you'll have 2 parallel lines that never intersect
you need a point of intersection to have a solution