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make one of the terms have the same number in both equations and then subtract.....
shall we start on this problem first? a) 38 = 2x - 5y 75 = 7x - 3y
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.
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.
\[-7(38=2x-5y)\] \[2( 75 = 7x - 3y )\]
welcome back :)
so can you distribute the -7 in the first equation and the 2 in the second equation ?
lol sorry i was having wifi problems
oh that's ok... my isp provider is bad too :P
are those correct?
I can check the second one without pen and paper... I need a calculator for the first xD
yeah they are.
now we can add these two equations together.
you will notice that the x's disappear and that's what we want.
so what is -266+
OH My bad what is -266+150 and 35y-6y
-266 + 150 = -116
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
what must we add?
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 :)
-116=29y now we just need division
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)
lol i really don't know what i just did there ^
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.
38 = 2x - 5y 75 = 7x - 3y try plugging in x = 9 and y = -4 to see if 38=38 and 75=75
then you know that your x and y values are correct.
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
so x=9 and y=-4 are our final answers?
but you need to rearrange the second equation... b) 6x + 5y = 22 3y= 4x + 36
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
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)
okay and then distribute?
24x+20y=88 -24x+18y=216 yes.. now we use addition to get rid of the x
do i add all of them or just 24x + (-24x)
you add all of them
yes the x cancels out.. you don't have to write 0 ... just 38y=304 and then we use division to have y = ?
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
is it easier to substitute into the 1st of 2nd equation? i was going to go with the 2nd but im not sure
substitution method works too, but your question is asking elimination method, so we're forced to do it that way.
i'm not very good at elimination lol
and i have my final exam tmrrw oh boyyyyy
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.
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
ok i'll go with the 2nd one
what is 3 x 8 ?
-4x+24=36 so we subtract 24 on both sides
idk why but i got confused
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
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
alright so now we have x = -3 and y = 8
now we can check 6x+5y=22 -4x+3y=36 x=-3 and y=8 must satisfy both of these equations
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!
:)...mathematics is always cumulative and requires a ton of practice.
yes i know and now the jokes on me for not doing my homework each night lol
just try your best :)
does your teacher use curved grading?
what's curved grading?
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.