Question

Which of these strategies would eliminate a variable in the system of equations?– 2y = 115.2 + 3y = -11

Answer 1

In order to eliminate a variable, let's check the resulting equation for each option:

A.

`\begin{gathered} \begin{cases}x-2y=11 \\ 5x-3y=-11\end{cases} \\ \\ x-2y+(5x-3y)=11+(-11) \\ 6x-5y=0 \end{gathered}`

B.

`\begin{gathered} -5(x-2y)+(5x-3y)=-5(11)+(-11) \\ -5x+10y+5x-3y=-55-11 \\ 7y=-66 \end{gathered}`

C.

`\begin{gathered} 5(x-2y)+(5x-3y)=5(11)+(-11) \\ 5x-10y+5x-3y=55-11 \\ 10x-13y=44 \end{gathered}`

So the only option where a variable is eliminated is option B.