Question

Solve the following system of equations:
x − 2y = 5
2x − 4y = 10

Answer 1

$\left\{\begin{array}{ccc}x-2y=5\\2x-4y=10&|divide\ both\ sides\ by\ (-2)\end{array}\right\\\\\underline{+\left\{\begin{array}{ccc}x-2y=5\\-x+2y=-5\end{array}\right}\\.\ \ \ \ \ \ \ \ \ \ \ 0=0-true\\\\Answer:infinitely\ many\ solutions\ \left\{\begin{array}{ccc}x\in\mathbb{R}\\y=\dfrac{x-5}{2}\end{array}\right$