How do you solve the following linear system: # 2x+y=0, 5x-y=7 #?

1 Answer
May 20, 2017

#x=1 and y=-2#

Explanation:

This is the best scenario you could hope for in a system of equations, because two of the variables are already additive inverses. #(+y) +(-y) =0#

We simply need to add the two equations together and the #y#-terms will be eliminated

#color(white)(..................)2x+y = 0#..............................A
#color(white)(..................)ul(5x-y = 7)#..............................B
#A+B: " "7x" "=7#
#color(white)(...................)x" " = 1#

Now that we know the value of #x#, plug it into #A or B# to find #y#

#color(white)(..................)2(1)+y = 0#..............................A
#color(white)(............................)y = -2#