Examine the consistency of the system of equations
`x + 2 y = 2" "``2x + 3y = 3`

Explanation

`x + 2 y = 2`

`2x + 3y = 3`

Write equation AX=B

`[[1,2],[2,3]][[x],[y]]=[[2],[3]]`

Here,

`A=[[1,2],[2,3]]`, `X=[[x],[y]]` & `B=[[2],[3]]`

Calculate `|A|`

`|A|=|[1,2],[2,3]|`

` " " " " " =3xx1-2xx2=3-4`

` " " " " " =-1`

` " " " " " ne0`

Since `|A|ne0`

`therefore` the system of equation is consistent.