Can you help me with my math homework??

Question

Solve the system

a+b=16
1/3a+1/4b=16

i cant get it every time it doesnt work!

Answer 1

*** The answer is a = 144, b = -128 ***

The QUICKEST way to get this is to DIVIDE the first equation by 4 before trying any elimination. Here's the subsequent working:
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(1/4)a + (1/4)b = 4 (Revised 1st equation.) 2nd one is:
(1/3)a + ((1/4)b = 16. Now subtract revised 1st eqn. from 2nd:
[(1/3 - 1/4)]a = 12, or (1/12)a = 12, so:
a = 144.

Then, from the original eqn. a + b = 16, b = 16 - 144 = -128.
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That's it!

NOW CHECK! (You should ALWAYS check your results back in the original question.):

144 + (- 128) = 16. Good;
(1/3)144 + (1/4)(-128) = 48 - 32 = 16 Great! --- they're BOTH satisfied.

Live long and prosper.

P.S. You'll notice that some responders have given you wrong "answers" that simply don't work in the original equations. (They didn't CHECK their results.) There's a moral here!

Answer 2

The first thing I would do is multiply everything in the second equation by three, 3(1/3a+1/4b=16) to get: a+3/4b=48. From there, you can use substitution or elimination.

Substitution:
First solve your new second equation, a+3/4b=48, for a to get: a=48 - 3/4b. You can then plug this value for a into the first equation, a+b=16, to get 48 - 3/4b+b=16. Simplify and you'll get 48+1/4b=16. Subtract 48 from both sides, which will leave you with 1/4b= - 32. Multiply each side by four to get: b= - 8. Plug the value you just found for b into the original first equation, a+b=16, and you'll get a - 8=16. Add 8 to both sides and you'll find that a=32.

Elimination: Mulitply you're new second equation by negative 1, -1(a+3/4b=48) to get: - a - 3/4b= - 48. You know have two equations which both have the same number of a but different signs. If you add these two equations they will cancel out:
a+b=16
+
- a - 3/4b = - 48
This will give you 1/4b= - 32. Multiply each side by 4, to get b= - 8. Plug the value you just found for b into the original first equation, a+b=16, and you'll get a - 8=16. Add 8 to both sides and you'll find that a=32.

Answer 3

multiply the bottom equation by 3 and you will have these two:
a + 3/4b = 48
a + b = 16

subtract the second from the first to get:
(3/4-1)b = 48-16
-1/4b = -32
b = 128

substituting into the second equation, a+ b = 16
a + 128 = 16
a = -112

Answer 4

(a+b=16
(1/3a+1/4b=16

a = 16 -b
1/3(16-b) + 1/4b = 16
16/3 - 1/3b + 1/4b - 16 = 0
64 - 4b + 3b - 192 = 0
-b = 128
b = -128
a + b = 16
a -128 = 16
a = 128 + 16
a = 144
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Answer 5

a+b=16
1/3a+1/4b=16

a= 16-b

1/3(16-b)+1/4b=16
16/3-1/3b+1/4b=16
-1/12b=32/3
b= -128

a=16-(-128)
a= 144

Answer 6

1 1 {16}

1/3 1/4 {16}

-----------------------------using matrices

1 1 {16}

0 -1/12 {32/3}
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1 1 {16}

0 1---{128}

--------------------------------------------
1 0 -112

0 1 128

therefore a= -112

b=128