# How do you solve the system using the elimination method for 2x - 4y =10 and -4x + 8y =-20?

Jul 6, 2015

Your system has $\infty$ solutions (it represents 2 coincident lines).

#### Explanation:

The second equation is equal to the first but multiplied by $- 2$!
The two equations represent two coincident lines that will have an $\infty$ number of points in common and consequently the system will have $\infty$ solutions as well.

If you want you can multiply the first by $2$ and add to the second;
{color(red)(4x-8y=20
{-4x+8y=-20 add the two together you get:
$0 = 0$ which is true.
This means that if you choose any set of coordinates that satisfy the first equation will satisfy the second as well:
For example:
$x = 1 \to y = - 2$ for the first:
$x = 1 \to y = - 2$ for the second as well!

$x = 2 \to y = - \frac{3}{2}$ for the first;
$x = 2 \to y = - \frac{3}{2}$ for the second as well;
...etc.