Question

Which is the best method to solve the following system of equations? A. SubstitutionB. EliminationC. GraphingD. None of the above

Answer 1

Elimination

Step-by-step explanation:

We subtract 2x from both sides of the second equation and get

`y-2x=2`

which we can also write as

`-2x+y=2`

multiplying both sides of this equation by 2 gives

`\begin{gathered} 2(-2x+y)=2*2 \\ \Rightarrow-4x+2y=4 \end{gathered}`

Hence, the system we have now is

`\begin{gathered} 5x-2y=1 \\ -4x+2y=4 \end{gathered}`

adding these two equations together gives

`\begin{gathered} 5x-2y=1 \\ -4x+2y=4 \\ ---------- \\ \boxed{x=5} \end{gathered}`

WIth the value of x in hand, we can now easily find the value of y.

`y=2x+2`
`y=2(5)+2`
`\boxed{y=12.}`

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.