How do you solve the following system?: # x - 3y = 0 , x = 1/2y + 3 #

1 Answer
Johnson Z.
Dec 20, 2015

point of intersection #=(18/5,6/5)#

Explanation:

When you solve a system, you are finding the point(s) at which the two lines intersect. We can solve a system by using elimination or substitution. In this case, we will use substitution.

To solve the system, we need to find the values of #x# and #y#. First, label your equations.

Equation #1#: #x-3y=0#
Equation #2#: #x=1/2y+3#

#1.# Start by substituting equation #2# into equation #1# to solve for #y#:

#x-3y=0#

#(1/2y+3)-3y=0#

#(1/2y+6/2)-6/2y=0#

#(y+6)/2-6/2y=0#

#(y+6-6y)/2=0#

#-5y+6=0#

#-5y=-6#

#y=6/5#

#2.# Now that you have the value of #y#, substitute #y=6/5# into either equation #1# or #2# to find the value of #x#. In this case, we will substitute it into equation #1#:

#x-3y=0#

#x-3(6/5)=0#

#x-18/5=0#

#x=18/5#

#:.#, the point of intersection is #(18/5,6/5)#.

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