Respuesta :

3(6x+2)-18x=12 (y=6x+2, so you plug in 6x+2 into the y in 3y-18x=12)
18x+6-18x=12    (Then you distribute the 3 to the 6x and to the 2)
6=12                    (Combine like terms 18x-18x)

There is no solution. Hope this helps and makes sense.

Answer:

The lines are parallel so no solution exist.

Step-by-step explanation:

Given : System of equations

[tex]y=6x+2[/tex] and [tex]3y-18x=12[/tex]

To find : What is the solution of the system?

Solution :

Let [tex]y=6x+2[/tex] ....(1)

[tex]3y-18x=12[/tex] ....(2)

Applying substitution method in the system of equations,

Substitute y from equation (1) into (2)

[tex]3y-18x=12[/tex]

[tex]3(6x+2)-18x=12[/tex]

[tex]18x+6-18x=12[/tex]

[tex]6\neq12[/tex]

Since by substitution we can't get the solution means either equations have no solution or both equations are parallel.

Re-write the equation (2)

[tex]3y-18x=12[/tex]

[tex]3(y-6x)=12[/tex]

[tex]y-6x=4[/tex]

[tex]y=6x+4[/tex]

Since the slope of both the equations are same.

The lines are parallel so no solution exist.