How do you tell whether the system #x + 2y = 10# and #2x + 4y = 10#has no solution or infinitely many solutions?

2 Answers
Bill Jorgensen
May 20, 2018

no solutions

Explanation:

you solve by elimination:

#x + 2y = 10#
#2x + 4y = 10#

#-2(x + 2y = 10)#
#2x + 4y = 10#

#-2x -4y = -20)#
#2x + 4y = 10#

add them together:

#0 = -10#

since this is not possible there are no solutions.

Jim G.
May 20, 2018

#"see explanation"#

Explanation:

#x+2y=10to(1)#

#2x+4y=10to(2)#

#"equation "(2)" is a multiple of equation "(1)#

#"thus they are parallel lines with no point of intersection"#

#"hence there is no solution"#

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