Question

How do you solve using the addition method and determine if the system is independant, dependant, inconsistant given 3/7x+5/9y=27 and 1/9x+2/7y=7?

Answer 1

`x=63` and `y=0`. The system is consistent and the equations are independent.

Explanation:

The system of equations is

`3/7x+5/9y=27`
`1/9x+2/7y=7`

Multiply the first equation by `-7"/"21` to eliminate `x`

`-7/27(3/7x+5/9y)=-7/27(27)`
`1/9x+2/7y=7`

This gives

`-1/9x-35/243y=-7`
`" "1/9x+2/7y" "=7`

Adding them together gives

`241/1701y=0 => y=0`

Plug `y=0` back into either of the original equations for `x`

`3/7x+5/9(0)=27`
`3/7x=27`
`x=27(7/3)`
`x=63`

If the lines intersect, then the system has one solution, given by the point of intersection. The system is consistent and the equations are independent.