Question

6. Select ALL the steps that would help to eliminate a variable and enablesolving for the system below: *-6x - y = 184x + 2y = 26Multiply the first equation by 2, then subtract the second equation from the resultMultiply the first equation by 4 and the second equation by 6, then subtract theresulting equationsMultiply the first equation by 2, then add the result to the second equationDivide the second equation by 2, then add the result to the first equationMultiply the second equation by 6, then subtract the result from the first equation

Answer 1

We need to solve the following system:

`\begin{cases}6x-y=18 \\ 4x+2y=26\end{cases}`

We need to select the steps that leads us to solving the system.

The first option says that we need to multiply the first equation by 2 then subtract the second equation from the result. Let's see how this goes:

`\begin{gathered} \begin{cases}(6x-y=18)\cdot2 \\ 4x+2y=26\end{cases} \\ \begin{cases}12x-2y=36 \\ 4x+2y=26\end{cases} \\ 12x-4x-2y-2y=36-26 \\ 8x-4y=10 \end{gathered}`

This does not eliminate one variable, therefore it's incorrect.

The second option tells us to multiply the first equation by 4 and the second by 6, then subtract the resulting equations:

`\begin{gathered} \begin{cases}(6x-y=18)\cdot4 \\ (4x+2y=26)\cdot6\end{cases} \\ \begin{cases}24x-4y=72 \\ 24x+12y=156\end{cases} \\ 24x-24x-4y-12y=72-156 \\ -16y=-84 \end{gathered}`

This eliminates one variable, therefore it is correct.

The third option tells us to multiply the first equation by 2, then add the result to the second equation.

`\begin{gathered} \begin{cases}(6x-y=18)\cdot2 \\ 4x+2y=26\end{cases} \\ \begin{cases}12x-2y=36 \\ 4x+2y=26\end{cases} \\ 12x+4x-2y+2y=36+26 \\ 16x=62 \end{gathered}`

This elimates one variable, therefore it is correct.

The fourth option tells us to divide the second equation by 2, then add the result to the first equation.

`\begin{gathered} \begin{cases}6x-y=18 \\ (4x+2y=26)\colon2\end{cases} \\ \begin{cases}6x-y=18 \\ 2x+y=13\end{cases} \\ 6x+2x-y+y=18+13 \\ 8x=31 \end{gathered}`

Since this eliminates one variable, it is correct.

The fith option tells us to multiply the second equation by 6, then subtract the result from the frist equation.

`\begin{gathered} \begin{cases}6x-y=18 \\ (4x+2y=26)\cdot6\end{cases} \\ \begin{cases}6x-y=18 \\ 24x+12y=156\end{cases} \\ 6x-24x-y-12y=18-156 \end{gathered}`

This does not eliminates one variable, it is incorrect.

The correct options are: 2, 3 and 4.