Solve by elimination. Check each solution.
a) 38 = 2x - 5y
75 = 7x - 3y
b) 6x + 5y = 22
3y= 4x + 36

- shelby1290

Solve by elimination. Check each solution.
a) 38 = 2x - 5y
75 = 7x - 3y
b) 6x + 5y = 22
3y= 4x + 36

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- theopenstudyowl

make one of the terms have the same number in both equations and then subtract.....

- shelby1290

@theopenstudyowl how do you do that?

- UsukiDoll

shall we start on this problem first?
a) 38 = 2x - 5y
75 = 7x - 3y

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## More answers

- 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

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

\[-7(38=2x-5y)\]
\[2( 75 = 7x - 3y )\]

- UsukiDoll

welcome back :)

- shelby1290

sure

- UsukiDoll

so can you distribute the -7 in the first equation and the 2 in the second equation ?

- shelby1290

lol sorry i was having wifi problems

- UsukiDoll

oh that's ok... my isp provider is bad too :P

- shelby1290

|dw:1434511952976:dw|

- shelby1290

|dw:1434512046087:dw|

- shelby1290

are those correct?

- UsukiDoll

I can check the second one without pen and paper... I need a calculator for the first xD

- UsukiDoll

yeah they are.

- UsukiDoll

\[-266=-14x+35y\]
\[150=14x-6y\]

- UsukiDoll

now we can add these two equations together.

- UsukiDoll

you will notice that the x's disappear and that's what we want.

- UsukiDoll

so what is -266+

- UsukiDoll

OH My bad
what is -266+150 and 35y-6y

- shelby1290

-266 + 150 = -116

- shelby1290

35y-6y=29y

- 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

what must we add?

- 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

-116=29y
now we just need division

- shelby1290

|dw:1434512501123:dw|

- 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

|dw:1434512671123:dw|

- shelby1290

lol i really don't know what i just did there ^

- 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

38 = 2x - 5y
75 = 7x - 3y
try plugging in x = 9 and y = -4 to see if 38=38 and 75=75

- UsukiDoll

then you know that your x and y values are correct.

- 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

so x=9 and y=-4 are our final answers?

- shelby1290

@UsukiDoll do i have to follow the same steps for part b?

- UsukiDoll

yes

- UsukiDoll

but you need to rearrange the second equation...
b) 6x + 5y = 22
3y= 4x + 36

- 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

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

okay and then distribute?

- UsukiDoll

yes :)

- shelby1290

|dw:1434515008507:dw|

- shelby1290

|dw:1434515088427:dw|

- UsukiDoll

24x+20y=88
-24x+18y=216
yes.. now we use addition to get rid of the x

- shelby1290

do i add all of them or just 24x + (-24x)

- UsukiDoll

you add all of them

- shelby1290

|dw:1434515403562:dw|

- 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

y=8

- 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

is it easier to substitute into the 1st of 2nd equation? i was going to go with the 2nd but im not sure

- shelby1290

or 2nd*

- UsukiDoll

substitution method works too, but your question is asking elimination method, so we're forced to do it that way.

- shelby1290

i'm not very good at elimination lol

- shelby1290

and i have my final exam tmrrw oh boyyyyy

- 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

okay

- 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

ok i'll go with the 2nd one

- UsukiDoll

-4x+3(8)=36

- UsukiDoll

what is 3 x 8 ?

- shelby1290

24

- UsukiDoll

-4x+24=36
so we subtract 24 on both sides

- shelby1290

|dw:1434516225078:dw|

- shelby1290

idk why but i got confused

- 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

-4x+24-24=36-24

- 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

|dw:1434516414467:dw|

- UsukiDoll

alright so now we have x = -3 and y = 8

- UsukiDoll

now we can check
6x+5y=22
-4x+3y=36
x=-3 and y=8 must satisfy both of these equations

- shelby1290

|dw:1434516608979:dw|

- 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

@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

:)...mathematics is always cumulative and requires a ton of practice.

- shelby1290

yes i know and now the jokes on me for not doing my homework each night lol

- UsukiDoll

just try your best :)

- shelby1290

thanks:)

- UsukiDoll

does your teacher use curved grading?

- shelby1290

what's curved grading?

- 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

http://academics.hamilton.edu/biology/smiller/curve.html

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