Two system of linear equation have same solution if and only if each equation in each system is a linear combination of the equations in other system? I didn't get it what are they trying to say?
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$\begingroup$Consider the system
\begin{align} x&=1 \tag{1}\\ y&=2 \tag{2} \end{align}
and
\begin{align} x+y&=3 \tag{3}\\ x-y&=-1 \tag{4} \end{align}
The two system shares the same solution. You can obtain $(3)$ by adding $(1)$ to $(2)$. You can also obtain $(4)$ by subtracting $(2)$ from $(1)$.
You should also recover $(1)$ and $(2)$ from linear combination of $(3)$ and $(4)$.
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