Question

What is the solution of the system? Use substitution.

y = 6x + 2
3y - 18x = 12

Answer 1

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 2

The lines are parallel so no solution exist.

Explanation:

Given : System of equations

`y=6x+2` and
`3y-18x=12`

To find : What is the solution of the system?

Solution :

Let
`y=6x+2` ....(1)

`3y-18x=12` ....(2)

Applying substitution method in the system of equations,

Substitute y from equation (1) into (2)

`3y-18x=12`

`3(6x+2)-18x=12`

`18x+6-18x=12`

`6\\eq12`

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)

`3y-18x=12`

`3(y-6x)=12`

`y-6x=4`

`y=6x+4`

Since the slope of both the equations are same.

The lines are parallel so no solution exist.