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.

$\begin{gathered} \frac{8x}{8}=\frac{80}{8} \\ x=10 \end{gathered}$

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).