System of equations
We want to solve the following system of equations:
[tex]\begin{gathered} x+2y=-20 \\ x+3y=-27 \end{gathered}[/tex]
We want to combine them. This means that we want to add them by columns:
we want to add the terms with x on one hand,
the terms with y on the other hand,
and the numbers.
If we leave the equations as they are and combine them, we would have:
We can obtain a better result if we multiply the first equation by -1, and combine them after that:
[tex]\begin{gathered} x+2y=-20 \\ \downarrow \\ -1(x+2y)=-1(-20) \\ -x-2y=20 \end{gathered}[/tex]
