# How to solve a system of two linear equations with two unknowns? {7(a+b)=b−a, 4(3a+2b)=b−8

How to solve a system of two linear equations with two unknowns?
$\left\{\begin{array}{l}7\left(a+b\right)=b-a\\ 4\left(3a+2b\right)=b-8\end{array}$
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ruinsraidy4
Here is a different approach:
$\left\{\begin{array}{l}7\left(a+b\right)=b-a\\ 4\left(3a+2b\right)=b-8\end{array}$
Then
$\left[\begin{array}{ccc}8& 6& 0\\ 12& 7& -8\end{array}\right]$ $⇔$ $\left[\begin{array}{ccc}1& 3/4& 0\\ 12& 7& -8\end{array}\right]$ $⇔$ $\left[\begin{array}{ccc}1& 3/4& 0\\ 0& -2& -8\end{array}\right]$ $⇔$ $\left[\begin{array}{ccc}1& 3/4& 0\\ 0& 1& 4\end{array}\right]$ $⇔$ $\left[\begin{array}{ccc}1& 0& -3\\ 0& 1& 4\end{array}\right]$
Resulting in $a=-3$ and $b=4$.
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Lustyku8
Try to perform algebra on both the equations till you have the 𝑎 and 𝑏 on one side and a number on the other. Then see if you can "combine" them together.