How do you solve the following linear system: #y = 3x - 2 , 14x - 3y = 0#?

1 Answer
May 8, 2018

Answer:

The solution is #(-6/5,-28/5)# or #(-1.2,-5.6)#.

Explanation:

Solve the linear system:

#"Equation 1":# #y=3x-2#

#"Equation 2":# #14x-3y=0#

The solution is the point #(x,y)# that the two lines have in common, which is the point of intersection. I'm going to use substitution to solve the system.

Equation 1 is already solved for #y#. Substitute #3x-2# for #y# in Equation 2 and solve for #x#.

#14x-3(3x-2)=0#

Expand.

#14x-9x+6=0#

Simplify.

#5x+6=0#

Subtract #6# from both sides.

#5x=-6#

Divide both sides by #5#.

#x=-6/5# or #-1.2#

Substitute #-6/5# for #x# in Equation 1. Solve for #y#.

#y=3(-6/5)-2#

Expand.

#y=-18/5-2#

Multiply #2# by #5/5# to get an equivalent fraction with #5# as the denominator.

#y=-18/5-2xx5/5#

#y=-18/5-10/5#

Simplify.

#y=-28/5# or #-5.6#

The solution is #(-6/5,-28/5)# or #(-1.2,-5.6)#.

graph{(y-3x+2)(14x-3y+0)=0 [-6.366, 4.73, -8.243, -2.696]}