Question

If 7a+3b=20 and 3a+7b=10, then what is the value of a+b?

Answer 1

`a+b=3`

Explanation:

We first have to solve the simultaneous equations:

`7a+3b=20` [A]
`3a+7b=10` [B]

[A] `-> a=(20-3b)/7` [C}

Replace for `a` in [B]:

`3((20-3b)/7) + 7b =10`

`(60-9b)/7 +7b=10`

Multiply through by 7:

`60-9b +49b=70`

`40b = 10 -> b=1/4 =0.25`

Replace for `b` in [C]:

`a= (20-3xx0.25)/7`

`= (20-0.75)/7 = 2.75`

This questions asks for the sum of `a` and `b`:

`a+b= 0.25+2.75 =3`