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

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Answer 1 · 2015-11-27T23:31:06

#RR#, all real numbers

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

#{(2x-10y=20),(-2x+10y=-20):}#

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

This means that the lines are the same line, so the answer is #RR#, or all real numbers.

If we look at the graphs:

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

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