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

1 Answer
Jul 6, 2015

Answer:

Your system has #oo# 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 #oo# number of points in common and consequently the system will have #oo# 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 -> y=-2# for the first:
#x=1-> y=-2# for the second as well!

#x=2 -> y=-3/2# for the first;
#x=2 -> y=-3/2# for the second as well;
...etc.