<s>[INST] The way to deduce the following equations. Given the $5$ equations.
$a_1=a_2+a_5 \tag{1}$
$a_4=a_3+a_5 \tag{2}$
$b=a_1+a_2 \tag{3}$
$b=a_3+\frac{a_4}{2} \tag{4}$
$\frac{a_5}{2}+a_1=a_3 \tag{5}$
I want to deduce the following.
$a_1=\frac{9}{16}*b\tag{6}$
$a_2=\frac{7}{16}*b\tag{7}$
$a_3=\frac{5}{8}*b\tag{8}$
$a_4=\frac{3}{4}*b\tag{9}$
$a_5=\frac{1}{8}*b\tag{10}$
Can anyone tell some hint(s)? so that I can deduce it in my own.
 [/INST] Hint 1: As the comments have stated, one approach is to write the system as a matrix and then find the RREF. The matrix is given by $$A = \left(
\begin{array}{cccccc}
 1 & -1 & 0 & 0 & -1 & 0 \\
 0 & 0 & 1 & -1 & 1 & 0 \\
 1 & 1 & 0 & 0 & 0 & b \\
 0 & 0 & 1 & \frac{1}{2} & 0 & b \\
 1 & 0 & -1 & 0 & \frac{1}{2} & 0 \\
\end{array}
\right)$$
You already have the result in your question, so know what the RREF should produce.
Hint 2: A second approach is to eliminate equations.
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