Question

Which of the following ordered pairs represents the solution to the system given below?2x + y = 204x − 2y = 40

Answer 1

The given system is

`\mleft\{\begin{aligned}2x+y=20 \\ 4x-2y=40\end{aligned}\mright.`

To solve this, we multiply the first equation by 2, then we sum equations.

`\mleft\{\begin{aligned}4x+2y=40 \\ 4x-2y=40\end{aligned}\mright.\rightarrow8x=80`

Then, we divide the equation by 8.

`\begin{gathered} (8x)/(8)=(80)/(8) \\ x=10 \end{gathered}`

Now, we use this value to find y.

`\begin{gathered} 2x+y=20 \\ 2(10)+y=20 \\ 20+y=20 \\ y=20-20 \\ y=0 \end{gathered}`

Therefore, the solution to the system is (10, 0).