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

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Answer 1 · 2017-05-17T03:43:07

$a + b = 3$ $a+b=3$

We first have to solve the simultaneous equations:

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

[A] $\to a = \frac{20 - 3 b}{7}$ $-> a=(20-3b)/7$ [C}

Replace for $a$ $a$ in [B]:

$3 (\frac{20 - 3 b}{7}) + 7 b = 10$ $3((20-3b)/7) + 7b =10$

$\frac{60 - 9 b}{7} + 7 b = 10$ $(60-9b)/7 +7b=10$

Multiply through by 7:

$60 - 9 b + 49 b = 70$ $60-9b +49b=70$

$40 b = 10 \to b = \frac{1}{4} = 0.25$ $40b = 10 -> b=1/4 =0.25$

Replace for $b$ $b$ in [C]:

$a = \frac{20 - 3 \times 0.25}{7}$ $a= (20-3xx0.25)/7$

$= \frac{20 - 0.75}{7} = 2.75$ $= (20-0.75)/7 = 2.75$

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

$a + b = 0.25 + 2.75 = 3$ $a+b= 0.25+2.75 =3$