Question

A+B=8 C+D=6 A+C =13 B+D=8 find the value A B C D ?

Answer 1

a + b = 8, (1)

c - d = 6, (2)

a + c = 13, (3)

b + d = 8. (4)

Add all four equations (1), (2), (3) and (4) (both sides). You will get

2a + 2b + 2c = 8 + 6 + 13 + 8 = 35, or

a + b + c = 17.5. (5)

Now distract eq.(1) from eq.(5). You will get

c = 17.5 - 8 = 9.5.

Next distract eq.(3) from eq.(5). You will get

b = 17.5 - 13 = 4.5.

Finally, from (1) a = 8-b = 8-4.5 = 3.5, and from (4) d = 8-b = 8-4.5 = 3.5.

Answer. a = 3.5, b = 4.5, c = 9.5, d = 3.5.