Evaluate in ONE Minute | Learn how to find the value of 2a-b-9c | College entrance exam

Can you find the value of 2a-b-9c in the given system of equations?

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Evaluate in ONE Minute | Learn how to find the value of 2a-b-9c | College entrance exam

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Learn how to find the value of 2a-b-9c

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[xof-woodworkinghobbyist]

I got the same result (yay!) by doing the following: 2 x (equation 1) + 3 x (equation 2)... Nice video as usual!

[amtrakatsfnyc]

I solved this by finding 3 equations: 2a=4+4b, b=2+3c, and 9c=3b-6. By subtraction using these equations and one substitution, the result is 10. Nice problem. Thank you.

[nineko]

Long time fan, first time commenter.

You took a very convoluted route, just multiply the first one by two, and the second one by three, and add those.

[mva]

a 2b = 2
2a - 4b = 4
b - 3c = 2
3b - 9c = 6
2a - 4b + 3b - 9c = 4 + 6 = 10
2a - b - 9c = 10

[SuperYoonHo]

Thanks so much sir these are really helping out my brain:)

[HappyFamilyOnline]

Very well explained👍
Thanks for sharing this awesome video😊

[roddurde]

2(a - 2b) = 2 x 2
2a - 4b = 4
2a = 4b + 4

2a - b - 9c
= 4b + 4 - b - 9c
= 3b - 9c + 4

b - 3c = 2
3b - 9c = 6

6 + 4 = 10

by an 8th grader :D

[alexniklas]

a-2b=2 times 2,
b-3c=2 times 3,
add the resulting expressions:
2a-4b=4;
3b-9c=6;
2a-4b + 3b-9c = 10;
2a-b-9c=10

[engralsaffar]

I did it by assigning a=0, and solving for b=-1 and c=-1

Therefore, 2(0)-(-1)-9(-1)=1+9=10

[SureshKotha]

Solved it like this
2a - b - 9c
= 2a - 4b + 4b - b - 9c
= 2(a - 2b) + 3b - 9c
= 2(2) + 3(b-3c)
= 4 + 3(2)
= 4 + 6 = 10

[prabhudasmandal]

I solved it simply like this we have a--2b=2 or a=2+2b again, we have b--3c=2 or c=(b--2)/3.now putting these values of a and c in the given expression we get 2(2+2b)--b--9.(b--2)/3.simplifying, it is 4+4b--b--3b+6=10 ans.

[owlsmath]

Nice problem! I don't think I've seen one quite like that before.

[NosztraiAdam]

I think it is a faster solution to try to match the variables like this: we need to find - 9c -> let's multiply by 3 x -3c in the definition so: 3 × (b - 3c ) = 3 x 2 -> 3b - 9c = 6 then you need 2a -> since we will make it equal with the previous definition and thus we will be on the other side of the equation we multiply by -2 -> -2 × ( a - 2b) = 2 × -2 -> -2a + 4b = -4 Since -4 is 10 less than 6 we can write the following equation: - 2a + 4b + 10 = 3b - 9c -> we add 2a and subtract -4b from the left side that gives us: 10 = 2a - b - 9c

[JSSTyger]

I believe the answer is achieved by doubling (a-2b) and tripling (b-3c). You add the results and end up with 10.

[johnbrennan]

a-3b=-3c. So -9c=3a-9b. Therefore 2a-b-9c= 2a-b+3a-9b=5a-10b=5(a-2b)=10

[johnbrennan]

a- 3b = -3c. Therefore -9c = 3a-9b. Substitute into 2a- b-9c and you get 2a-b +3a-9b = 5a -10b. But a-2b= 2. So5a- 10b= 10.

[theuserbl]

Why going the way over the equation a - 6c = 6 ?

It goes more straight direct:

a - 2b = 2
b - 3c = 2

how many a's are needed? 2. So multiply the first equation with 2:
2a - 4b = 4
How many b's are needed? -1. I have now -4. How many are needed to come to -1? Adding 3.
How many b's are in the second equation? 1. With which factor must it be multiplied to come to 3? With 3.
3b - 9c = 6

And now the two equations can be added together:
2a -b -9c = 10

[devondevon]

answer =10
a-2b =2
2a-4b=4 x 2
2a= 4+4b
[4+4b-b] -9c =?
4+3b -9c?
since b-3c =2 given, then
3b-9c =6 x 3 ( ie multiply the above by 3) hence
4+ 6= ?
10 answer

[mindstreamx]

Since we need 2a and 9c, you can just multiply eqn (1) by 2 and eqn (2) by 3 and finally add them.