Answer:
Elimination
Explanation:
We subtract 2x from both sides of the second equation and get
[tex]y-2x=2[/tex]
which we can also write as
[tex]-2x+y=2[/tex]
multiplying both sides of this equation by 2 gives
[tex]\begin{gathered} 2(-2x+y)=2\times2 \\ \Rightarrow-4x+2y=4 \end{gathered}[/tex]
Hence, the system we have now is
[tex]\begin{gathered} 5x-2y=1 \\ -4x+2y=4 \end{gathered}[/tex]
adding these two equations together gives
[tex]\begin{gathered} 5x-2y=1 \\ -4x+2y=4 \\ ---------- \\ \boxed{x=5} \end{gathered}[/tex]
WIth the value of x in hand, we can now easily find the value of y.
[tex]y=2x+2[/tex][tex]y=2(5)+2[/tex][tex]\boxed{y=12.}[/tex]
Hence, the solution to the system is (x,y) = (5, 12).
In solving our system we used the elimination method since it was the best method to use for our system. Therefore, choice B is the correct answer.
