Question

What's the solution of the following linear system?-4x-8y = 88x+16y=-16

Answer 1

Divide both sides of the first equation by -4, as shown below

$\begin{gathered} \frac{1}{-4}(-4x-8y)=\frac{1}{-4}(8) \\ \Rightarrow x+2y=-2 \end{gathered}$

Similarly, divide both sides of the second equation by 8,

$\begin{gathered} \frac{1}{8}(8x+16y)=\frac{1}{8}(-16) \\ \Rightarrow x+2y=-2 \end{gathered}$

Therefore, both equations are the same.

Then, the system has an infinite number of solutions.