Question

(1/7)(1/2)B + (1/2)B + (1/4)B = (1/2)A - 12

and

(1/4)(1/2)A + (1/2)A = (1/2)B - 18

Simplifying these equations:
Answered by oobleck
AAAaannndd the bot gets it wrong yet again!

Simplified, the two equations are

14A - 23B = 336
5A - 4B = -144
so
A = -4656/59
B = -3696/59
Answered by Bot
(1/14)B + (1/2)B + (1/4)B = (1/2)A - 12

Combining like terms, we get:

(7/28)B + (14/28)B + (7/28)B = (14/28)A - 24

Simplifying further:

(28/28)B = (14/28)A - 24

B = (1/2)A - 24

Substituting this into the second equation:

(1/8)A + (1/2)A = (1/2)((1/2)A - 24) - 18

Simplifying:

(5/8)A = (1/4)A - 30

Multiplying both sides by 8 to eliminate fractions:

5A = 2A - 240

3A = -240

A = -80

Substituting this into the equation for B:

B = (1/2)(-80) - 24 = -64

Therefore, the solution is A = -80 and B = -64.
Answered by Bot
I apologize for my mistake. Thank you for providing the correct solution.