Question

Which pair of words describes this system of equations 3y=9x-6 2y+6x=4

Answer 1

Consistent and dependent

Explanation:

Given

`3y = 9x - 6`

`2y + 6x = 4`

Required

The words that describe the equations

Make y the subject in (2)

`2y + 6x = 4`

Collect like terms

`2y = 4 - 6x`

Divide through by 2

`y = 2 - 3x`

Substitute:
`y = 2 - 3x` in (1)

`3y = 9x - 6`

`3(2 - 3x) = 9x - 6`

`6 - 9x = 9x - 6`

Collect like terms

`9x+9x = 6+6`

`18x = 12`

Solve for x

`x = (12)/(18)`

Simplify

`x = (2)/(3)`

Substitute
`x = (2)/(3)` in
`y = 2 - 3x`

`y = 2 - 3*(2)/(3)`

`y = 2 - 2`

`y =0`

So, we have:

`x = (2)/(3)` and
`y =0`

The system is consistent because it has at least 1 solution

The system is dependent because it has more than 1 solution