How do you solve the system : #2x+6y=5#, #8x+24y=20#?

1 Answer
Aug 23, 2017

Answer:

Infinitely many solutions

Explanation:

Hello there!

#2x + 6y = 5#
#8x + 24y = 20#

You can solve the system by using the elimination form or you can use the substitution form. I like substitution so I'll use it :)

We need to solve #2x + 6y = 5# for x
#2x + 6y = 5#
#2x = -6y + 5#
Divide both sides by 2
#(2x)/2# = #(-6y+5)/2#
#x# = #-3y# +#5/2#
Now substitute #-3y# +#5/2# for #x# in #8x +24y = 20#
#8# #(-3y + 5/2)# + #24y = 20#
Distribute
#(8)(-3y) + (8)(5/2) + 24y = 20#
#-24y + 20 + 24y_ = 20#
#20 = 20#
Add -20 to both sides
#20 - 20 = 20 - 20#
#0 = 0#
Final answer: All real numbers are solutions

I hope I helped!