Which one of the following is the solution to the equation $9x-5y=6?$

Given: $9x-5y=6$

The points which satisfy an equation are the solution of the equation.

Putting (4,3) in the equation, we get,

$9\times 4-5\times 3=6$

$21\ne 6$

∵ LHS$\ne$RHS

Thus, (4,3) is not the solution of the given equation.

Now putting (4,6) in the equation, we get,

$9\times 4-5\times 6=6$

$36-30=6$

$6=6$

∵ LHS = RHS

Thus, the solution of the equation is (4,6).

Putting (3,2) in the equation, we get,

$9\times 3-5\times 2=6$

$17\ne 6$

∵ LHS$\ne$RHS

Thus, (3,2) is not the solution of the given equation.

Putting (6,5) in the equation, we get,

$9\times 6-5\times 5=6$

$11\ne 6$

∵ LHS$\ne$RHS

Thus, (6,5) is not the solution of the given equation.

Therefore, (4,6) is the correct solution.