Question

Solve the system of equations:3x - 4y = 202x + 4y = 0Group of answer choicesx = 2, y = 4x = -2, y = 4

Answer 1

Given the system of equations:

`\begin{cases}3x-4y=20 \\ 2x+4y=0\end{cases}`

Add up both equations:

`\begin{gathered} \begin{cases}3x-4y=20 \\ 2x+4y=0\end{cases}\rightarrow3x+2x-4y+4y=20+0 \\ \rightarrow5x=20 \end{gathered}`

Solve for x,

`\begin{gathered} 5x=20\rightarrow x=(20)/(5) \\ \Rightarrow x=4 \end{gathered}`

Plug the value of x in equation 2 and solve for y,

`\begin{gathered} 2x+4y=0\rightarrow2(4)+4y=0\rightarrow8+4y=0 \\ \rightarrow4y=-8\rightarrow y=-(8)/(4) \\ \Rightarrow y=-2 \end{gathered}`

Thereby,

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