How do you solve x-5y=10, -2x+10y=-20?

Nov 27, 2015

$\mathbb{R}$, all real numbers

Explanation:

Multiply the first equation by $2$. This give us:

$\left\{\begin{matrix}2 x - 10 y = 20 \\ - 2 x + 10 y = - 20\end{matrix}\right.$

However, when we add these, we get $0 + 0 = 0$.

This means that the lines are the same line, so the answer is $\mathbb{R}$, or all real numbers.

If we look at the graphs:

$x - 5 y = 10$
graph{x-5y=10 [-10, 10, -5, 5]}

$- 2 x + 10 y = - 20$
graph{-2x+10y=-20 [-10, 10, -5, 5]}