If `|{:(2,-y),(1,x):}|=16` and `|{:(3,2),(y,x):}|=3`. From the given determinant form two simultaneous equations and solve them.

Explanation

`|{:(2,-y),(1,x):}|=16` `|{:(3,2),(y,x):}|=3`
`{:( :.2xx(x)-(-y)xx1=16,:.3xx x-2xxy=3):}`
`{:( :.2x+y=16…..(1), :. 3x-2y=3……(2)):}`
Multiplying equation `(1)` by `2`,
`4x+2y=32`…….`(3)`
Adding equations `(2)` and `(3)`,
`{:(3x-2y=3" ...(2)"),(4x+2y=32" ...(3)"),(bar(""7x" "="25")):}`
`{:( :. x=(35)/(7), :. x=5):}`
Substituting `x=5` in equation `(1)` ,
`{:(2(5)+y=16, :.10+y=16, :. y=16-10, :.y=6):}`