Question

question 6
why is elimination a good method for solving this system of equations?
$2x + 6y = 20$
$-2x + 3y = 10$
since the first equation contains $2x$ and the second equation contains $-2x$, the equations can be subtracted, leaving only a term with the variable $y$ equal to an integer.
we can halve equation 1, and then subtract it from equation 2. this leaves only a term with the variable $x$ and a term with the variable $y$.
since the first equation contains $2x$ and the second equation contains $-2x$, the equations can be added together, leaving only a term with the variable $y$ equal to an integer.
we can double equation 2 and then subtract it from equation 1. this leaves only a term with the variable $x$ and a term with the variable $y$.

Explanation:

Elimination works by removing one variable. Here, the $x$-terms are $2x$ and $-2x$, which sum to 0. Adding the two equations eliminates $x$, leaving only a term with $y$ and an integer, simplifying solving for the variable.

Answer:

Since the first equation contains $2x$ and the second equation contains $-2x$, the equations can be added together, leaving only a term with the variable $y$ equal to an integer.