Systems of equations by substitution help

Question

I'm trying to solve a systems of equations problem but I can't seem to see what I'm doing wrong... As far as I can tell the way to solve a system of equations by substitution involves the following steps.

1. Isolate a variable in one of the equations
2. substitute that isolated variable into equation two so that you're second equation is in one variable
3. solve equation two for the second unknown variable
4. use the result from the second equation to find out what your original isolated variable equals.

here's my problem and what I tried:

equation 1: $1 = A + B$

equation 2: $8 = 5A + 2B$

Isolating $B$

$B = 1 - A$

Solving for A

$8 = 5A + 2(1-A)$

$\Rightarrow 8 = 5A + 2 - 2A$

$\Rightarrow8 = 3A + 2$

$\Rightarrow6 = 3A$

$\Rightarrow A = 1/2$

substituting back for $B$

$\Rightarrow B = 1 - 1/2$

$\Rightarrow B = 1/2$

final answer: $(A,B) = (1/2,1/2)$

according to wolfram alpha this is incorrect. can anyone tell me where I went wrong? thanks.

Answer 1

A=1/2 is the wrong conclusion from preceding step

A=2

The rest is all fine .

Answer 2

$6 = 3A$

$\Rightarrow A = 2$

$\Rightarrow B = -1$