Question

need help to write up a linear system of two equations: If 'B' gives 'A' four, 'A' will have three times as many as 'B'. If 'A' gives 'B' four, both will have the same amount. How many does each have? I'd appreciate to see the work on setting up this problem, as my previous attempts at solving the system were incorrect(negative).

Answer 1

First step to such problems is to represent, right?
We can let
A = the number "A" initially has
B = the number "B" initially has

Answer 2

if "B" gives "A" four, then "B" would have
B - 4
and "A" would have
A + 4

and if "B" gives "A" four, "A" will have three times as many as "B"
Thus:
\[3(B - 4) = A + 4 \]

Answer 3

if "A" gives "B" four, then "A" would have
A - 4
and "B" would have
B + 4

and if "A" gives "B" four, both will have the same amount
Thus:
\[A - 4=B+4\]

Answer 4

Thank you so much....crossing my fingers for tomorrow :)