How do you solve the following linear system: # 6x+y =3, 2x+3y=5 #?

1 Answer
Mar 4, 2018

Answer:

#x=1/4, y=3/2#

Explanation:

In this case, we can use substitution, but I find using elimination simpler. We can see that if we do a little work, subtracting the two equations will let us solve for #y#.

#E_1: 6x+y=3#

#E_2: 2x+3y=5#

#E_2: 3(2x+3y)=3*5#

#E_2: 6x+9y=15#

#E_1-E_2: 6x+y-(6x+9y)=3-15#

#6x-6x+y-9y=-12#

#-8y=-12#

#y=(-12)/(-8)=3/2#

Now we plug in the solution to #y# into #E_1# to solve for #x#:

#E_1: 6x+3/2=3#

#6x=3-3/2#

#6x=3/2#

#x=(3/2)/6=3/12=1/4#