The idea is multiply one or both equations by a number or numbers such that the coefficients of x or y in each equation will cancel when the two equations are added (or subtracted).
6x - 5y = 3 [1]
-12x + 8y = 5 [2]
"[1]" and "[2]" are just means to refer to each equation. Read "[1]" as "the first equation".
If we multiply [1] by 2, we will be able to eliminate the x's upon adding the two equations.
[1] * 2: 12x - 10y = 6 [3]
and [2] is still: -12x + 8y = 5
See that if we now add [2] and [3], the x's cancel:
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