shelby1290
  • shelby1290
Solve by elimination. Check each solution. a) 38 = 2x - 5y 75 = 7x - 3y b) 6x + 5y = 22 3y= 4x + 36
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
theopenstudyowl
  • theopenstudyowl
make one of the terms have the same number in both equations and then subtract.....
shelby1290
  • shelby1290
@theopenstudyowl how do you do that?
UsukiDoll
  • UsukiDoll
shall we start on this problem first? a) 38 = 2x - 5y 75 = 7x - 3y

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UsukiDoll
  • UsukiDoll
so... let's eliminate the x first we do this through multiplication.. the first equation must be negative because when we add numbers... for example if I have -7x +7x the x cancels out... so looking at the x term only we have 2x and 7x.
UsukiDoll
  • UsukiDoll
I need to multiply the first equation by -7 and multiply the second equation by 2 because our goal is to create the same number and if we're going to add..at least one of the numbers must be negative to get rid of our x.
UsukiDoll
  • UsukiDoll
\[-7(38=2x-5y)\] \[2( 75 = 7x - 3y )\]
UsukiDoll
  • UsukiDoll
welcome back :)
shelby1290
  • shelby1290
sure
UsukiDoll
  • UsukiDoll
so can you distribute the -7 in the first equation and the 2 in the second equation ?
shelby1290
  • shelby1290
lol sorry i was having wifi problems
UsukiDoll
  • UsukiDoll
oh that's ok... my isp provider is bad too :P
shelby1290
  • shelby1290
|dw:1434511952976:dw|
shelby1290
  • shelby1290
|dw:1434512046087:dw|
shelby1290
  • shelby1290
are those correct?
UsukiDoll
  • UsukiDoll
I can check the second one without pen and paper... I need a calculator for the first xD
UsukiDoll
  • UsukiDoll
yeah they are.
UsukiDoll
  • UsukiDoll
\[-266=-14x+35y\] \[150=14x-6y\]
UsukiDoll
  • UsukiDoll
now we can add these two equations together.
UsukiDoll
  • UsukiDoll
you will notice that the x's disappear and that's what we want.
UsukiDoll
  • UsukiDoll
so what is -266+
UsukiDoll
  • UsukiDoll
OH My bad what is -266+150 and 35y-6y
shelby1290
  • shelby1290
-266 + 150 = -116
shelby1290
  • shelby1290
35y-6y=29y
UsukiDoll
  • UsukiDoll
we need to use addition because we want the -14x+14x to cancel out. yes that's correct -266+150=-116 and yes 35y-6y=29y
shelby1290
  • shelby1290
what must we add?
UsukiDoll
  • UsukiDoll
we need to use addition so that the -14x and the 14x cancel out... we need to use addition for the first and second equation... you're doing good so far :)
UsukiDoll
  • UsukiDoll
-116=29y now we just need division
shelby1290
  • shelby1290
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UsukiDoll
  • UsukiDoll
very good! :) luckily that was the hard part of doing this problem... once we have one of our variables we can just solve for x We can choose to substitute y=-4 in one of these equations 38 = 2x - 5y 75 = 7x - 3y I think using the first equation will be easier 38 = 2x - 5(-4)
shelby1290
  • shelby1290
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shelby1290
  • shelby1290
lol i really don't know what i just did there ^
UsukiDoll
  • UsukiDoll
that's good :) if you have x = 9 and y = -4 plug it back into those two equations... if you have 38=38 it's correct... and you have the right x and y values.
UsukiDoll
  • UsukiDoll
38 = 2x - 5y 75 = 7x - 3y try plugging in x = 9 and y = -4 to see if 38=38 and 75=75
UsukiDoll
  • UsukiDoll
then you know that your x and y values are correct.
UsukiDoll
  • UsukiDoll
38 = 2(9) - 5(-4) 38=18+20 38=38 75 = 7(9) - 3(-4) 75= 63+12 75=75 so our answer is correct :) x = 9 and y = -4
shelby1290
  • shelby1290
so x=9 and y=-4 are our final answers?
shelby1290
  • shelby1290
@UsukiDoll do i have to follow the same steps for part b?
UsukiDoll
  • UsukiDoll
yes
UsukiDoll
  • UsukiDoll
but you need to rearrange the second equation... b) 6x + 5y = 22 3y= 4x + 36
UsukiDoll
  • UsukiDoll
you just have to subtract 4x on both sides and switch places I'll do that part for you 3y-4x=4x-4x+36 3y-4x=36 -4x+3y=36 so now you have 6x+5y=22 -4x+3y=36
UsukiDoll
  • UsukiDoll
we could get rid of the x again see we already have a negative sign on the second equation .. so we multiply the 4 throughout the first equation and 6 throughout the second equation 4(6x+5y=22) 6(-4x+3y=36)
shelby1290
  • shelby1290
okay and then distribute?
UsukiDoll
  • UsukiDoll
yes :)
shelby1290
  • shelby1290
|dw:1434515008507:dw|
shelby1290
  • shelby1290
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UsukiDoll
  • UsukiDoll
24x+20y=88 -24x+18y=216 yes.. now we use addition to get rid of the x
shelby1290
  • shelby1290
do i add all of them or just 24x + (-24x)
UsukiDoll
  • UsukiDoll
you add all of them
shelby1290
  • shelby1290
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UsukiDoll
  • UsukiDoll
yes the x cancels out.. you don't have to write 0 ... just 38y=304 and then we use division to have y = ?
shelby1290
  • shelby1290
y=8
UsukiDoll
  • UsukiDoll
alright... since we have y=8, we can choose to place y=8 in the first or second equation... 6x+5y=22 -4x+3y=36
shelby1290
  • shelby1290
is it easier to substitute into the 1st of 2nd equation? i was going to go with the 2nd but im not sure
shelby1290
  • shelby1290
or 2nd*
UsukiDoll
  • UsukiDoll
substitution method works too, but your question is asking elimination method, so we're forced to do it that way.
shelby1290
  • shelby1290
i'm not very good at elimination lol
shelby1290
  • shelby1290
and i have my final exam tmrrw oh boyyyyy
UsukiDoll
  • UsukiDoll
elimination method for these equations means that we either need the x to cancel or the y to cancel... so we need to use multiplication and figure out what number do I need to multiply to have at least one of the x's and y's to be the same. we need to have at least one positive number and one negative number so when we add the x or the y should cancel.
shelby1290
  • shelby1290
okay
UsukiDoll
  • UsukiDoll
so getting back to 6x+5y=22 -4x+3y=36 since we have y = 8 we can choose one of these equations and solve for x
shelby1290
  • shelby1290
ok i'll go with the 2nd one
UsukiDoll
  • UsukiDoll
-4x+3(8)=36
UsukiDoll
  • UsukiDoll
what is 3 x 8 ?
shelby1290
  • shelby1290
24
UsukiDoll
  • UsukiDoll
-4x+24=36 so we subtract 24 on both sides
shelby1290
  • shelby1290
|dw:1434516225078:dw|
shelby1290
  • shelby1290
idk why but i got confused
UsukiDoll
  • UsukiDoll
well we need to shift the 24 to the right, so to do that I need to subtract because I want to get rid of the 24 on the left
UsukiDoll
  • UsukiDoll
-4x+24-24=36-24
UsukiDoll
  • UsukiDoll
24-24 is 0 so the 24 is no longer on the left side... but I do have 24 on the right side which is what I need -4x=36-24
shelby1290
  • shelby1290
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UsukiDoll
  • UsukiDoll
alright so now we have x = -3 and y = 8
UsukiDoll
  • UsukiDoll
now we can check 6x+5y=22 -4x+3y=36 x=-3 and y=8 must satisfy both of these equations
shelby1290
  • shelby1290
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UsukiDoll
  • UsukiDoll
the second one seems easier to check -4(-3)+3(8) = 36 12+24=36 36=36 6(-3)+5(8)=22 -18+40=22 22=22 yay!
shelby1290
  • shelby1290
@UsukiDoll thanks for all of the help and remaining patient with me. I'm so nervous for my final exam tomorrow. I'm not the best at math at all!
UsukiDoll
  • UsukiDoll
:)...mathematics is always cumulative and requires a ton of practice.
shelby1290
  • shelby1290
yes i know and now the jokes on me for not doing my homework each night lol
UsukiDoll
  • UsukiDoll
just try your best :)
shelby1290
  • shelby1290
thanks:)
UsukiDoll
  • UsukiDoll
does your teacher use curved grading?
shelby1290
  • shelby1290
what's curved grading?
UsukiDoll
  • UsukiDoll
instead of grading A B C D F.. curved grading is used to give more students who think they are going to fail , better grades... so a 80-100 will end up being an A instead of 90-100 being an A on regular grading.
UsukiDoll
  • UsukiDoll
http://academics.hamilton.edu/biology/smiller/curve.html

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