As a general rule: if you find two opposite coefficients for the same variable, it is convenient to add. If you find two equal coefficients for the same variable, it is convenient to subtract.
In the first system, the coefficients of [tex]y[/tex] are -2 and +2. If you add those you get 0, and thus you eliminate the variable.
In the second system, the coefficient of [tex]x[/tex] is 6 in both equation. If you subtract those you get 0, and thus you eliminate the variable.
