If 5a – 3b = –9 and 3a + b = 31, then a + b =

Question

A) –7

B) –3

C) 6

D) 13

E) 19

PKN · Answer

Elimination method:-
Multiply equation (1) with 3 and equation (2) with 5, then subtracting (2) from (1), we have 
 3*(5a – 3b = –9) --------(1)
 5*(3a + b = 31) --------(2)
 (-) (-) (-)
.......................................................
 -14b = -182
or, b= \frac{-182}{-14} =13

from (2) we have, 3a=31-b
 or, a= \frac{(31-b)}{3} 
Now substituting the value of b, we have 
 a= \frac{(31-13)}{3} = \frac{18}{3} =6

So, we have a+b=6+13=19.

Hence, Option (E) is the answer.

generis · Answer

Given:
5a – 3b = –9 ...(P)
3a + b = 31 ....(Q)

Multiply (Q) by 3 to get (R), then add (P) and (R)

5a – 3b = –9 ...(P)
9a + 3b = 93 ...(R)
-------------------
14a = 84
a = 6

Find b

From (Q): 3a + b = 31

(3)(6) + b = 31
b = (31-18) = 13

(a + b) = (6 + 13) = 19

Answer E

pushpitkc · Answer

Given:   5a – 3b = –9 and 3a + b = 31

Rearranging the second equation we get b = 31 - 3a

Substituting this value of b in the first equation.
5a - 3(31 - 3a) = -9 -> 14a - 93 = -9 -> 14a = 84 -> a = 6 | b = 31 - 18 = 13

Therefore, a+b = 6+13 =  19(Option E)

Chethan92 · Answer

5a-3b = -9.............(1)
3a+b = 31.............(2)

Multiply (1) by 3 and (2) by 5, then

15a-9b = -27
15a+5b = 155
subtract (1) from (2); 14b = 182, b = 13,
a = 6
a+b = 19

Bunuel · Answer

If you add you'd get 30a -4b = 128. You should subtract.

Chethan92 · Answer

oh yes. silly mistake

KSBGC · Answer

Given,

3a + b = 31

b = 31 - 3a.

again

5a - 3b = -9

5a - 3(31 - 3a) = -9

5a - 93 + 9a = -9

14a = 84.

a = 6.

we know,

3a + b = 31

3*6 + b = 31

18 + b = 31

b = 31 - 18

b = 13.

Now we have ,

a = 6

b = 13.

a + b = 6 +13 = 19.

E is the correct answer.

Pimpmybear · Answer

Is there a shorter solution? 
My solution: 
1) add two equations 
5a - 3b + 3a + b = 31 - 9
8a - 2b = 22
4a - b = 11 => b = 4a - 11

2) find a and b by plugging b into any of them
5a - 12a + 33 = - 9 
7a = 42
a = 6 => b = 31-18 = 13

Answer: a+b = 13+6 = 19. Choice E

Archit3110 · Answer

solve for two given eqns

5a − 3b = −9 and 3a + b = 31
we get a = 6
and b = 13
a+b=19
IMO E

bumpbot · Answer

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If 5a – 3b = –9 and 3a + b = 31, then a + b =

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If 5a – 3b = –9 and 3a + b = 31, then a + b =

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