How do you solve using the elimination method #3x + 4y = 5#, #6x + 8y = 10#?

1 Answer
Sep 1, 2015

Answer:

This system of equations has an infinite number of solutions.

Explanation:

Your system of equations looks like this

#{(3x + 4y = 5), (6x + 8y = 10) :}#

Notice that if you multiply the first equation by #(-2)# and then add the left-hand sides and the right-hand sides separately, you will get

#{(3x + 4y = 5 | * (-2)), (6x + 8y = 10) :}#

#{(-6x - 8y = -10), (6x " "+ 8y = " "10) :}#
#stackrel("---------------------------------------------")#
#" "0 " "+ 0 " "= 0#

Since you end up with #0=0#, which is an equality that does not depends on any variable, the system of equations will have an infinite number of solutions.

You can think of a system of equations as describing two lines. In your case, both equations decribe the same line, because if you multiply the first equation by #2# you get the second equation

#{(6x + 8y = 10), (6x + 8y = 10) :}#

This implies that you have an infinite number of #(x,y)# points that correspond to this line.