Solving a 'Harvard' University entrance exam question

[00:00:00]Hello Friends find the value of 'a' and 'b' If 150a+190b=1760 let's have a solution so, we have a problem of '150a+190b=1760' which can be solved by dividing '10' on both sides 150a/10+190b/10=1760/10 '0' cancels It will be 15a+19b=176 It can be written as 15a=176-19b divide by '15' on both sides 15a/15=(176-19b)/15 '15' cancels a=(176-19b)/15 (say this is first equation) a=(150+26-15b-4b)/15 separate it into fractions, a=(150-15b)/15+(26-4b)/15 a=15(10-b)/15+(26-4b)/15 where '15' cancels a=10-b+(26-4b)/15 let m=(26-4b)/15 multiply by '15' on both sides 15.m=15.(26-4b)/15 '15' cancels 15m=26-4b 4b=26-15m divide by '4' on both sides 4b/4=(26-15m)/4 '4' cancels b=(26-15m)/4 (say this is second equation) b=(24+2-12m-3m)/4 b=(24-12m)/4+(2-3m)/4 b=4(6-3m)/4+(2-3m)/4 '4' cancels b=6-3m+(2-3m)/4 let n=(2-3m)/4 multiply by '4' on both sides 4.n=4.(2-3m)/4 '4' cancels 4n=2-3m in the next step 3m=2-4n divide by '3' on both sides 3m/3=(2-4n)/3 '3' cancels m=(2-4n)/3 (say this is third equation) m=(2-3n-n)/3 m=-3n/3+(2-n)/3 '3' cancels m=-n+(2-n)/3 let t=(2-n)/3 multiply by '3' on both sides 3.t=3.(2-n)/3 '3' cancels 3t=2-n in the next step n=2-3t If t=0 then n=2-3(0) 3x0=0 n=2 recall third equation m=(2-4n)/3 put n=2 m=(2-4(2))/3 m=(2-8)/3 m=-6/3 m=-2 recall second equation b=(26-15m)/4 put m=-2 b=(26-15(-2))/4 b=(26+30)/4 b=56/4 4x14=56 b=14 recall first equation a=(176-19b)/15 put b=14 a=(176-19(14))/15 in the next step a=(176-266)/15 a=-90/15 15x6=90 a=-6 so finally, a=-6 and b=14 in the last step, I'm going to verify 150a+190b=1760 putting values of 'a' and 'b' 150(-6)+190(14)=1760 -900+2660=1760 1760=1760 you can see, L.H.S=R.H.S which shows that the values of a=-6 and b=14 satisfies this equation of '150a+190b=1760' thanks for watching this video please subscribe this channel to get the notification of my new videos ok bye